I attempt to directly answer all of your questions at the bottom of this answer. But before that, here are 7 points or aspects of learning stack-based Forth, or generally about stack-based-languages, or ways to proceed with your goals:
1: Here is a key way to think about this: The stack is not the place where you keep your data -- just the way that you pass parameters from one function (or method) to another.
2: There is a "Basic Language" interpreter written in Forth. This would be one way to write an application in Forth -- write your own Basic interpreter (or type in one you find), then write the Roguelike game in the Basic language you just created.
3: If you go through the old "Forth Dimensions" magazine, several different object-oriented extensions to Forth were created and presented (including source code). Type one of those in, and use it to write your rogue-like game in one of those object-oriented ways. If you're still stuck, write it in your favorite C language -- C++, C#, or Java, and here's the key... write it as primitively as you can. Then take your own application apart -- each method, enum, constant, etc. constitutes part of a Domain Specific Language that you created in order to implement the game. Write down those parts, and figure out how to do it in Forth, ideally using only the idioms of Forth. You may have to work in Forth a while to get to that stage.
4: Learn how to program in assembly language, an assembly language for which a Forth exists that has an embedded assembler for the same microcontroller or CPU. This is where Forth really crushed the competition when computers were just becoming more widely available -- bringing a completely new microcontroller up, creating the BIOS and the OS. Once you've done this in pure assembly language, then go into the Forth that has the same assembly language and program the same application, but using the Forth assembler to build the building blocks (the DSL's) and then writing the BIOS and the OS in those DSL's. Forths happen to be both low-level and high-level at the same time, and the best-written applications are written in multiple DSL's, not in stack-based primitives. Once you've written in assembly language, when you try to learn Forth, you will find that it is easy -- the basic mechanisms are simple, but the combination of basic mechanisms is simple, powerful and elegant.
5: Look at either C# or Java, and realize that they are both based on Virtual Machines, which is a specific kind of DSL. But also realize that both Virtual Machines are stack machines, and the language that powers both of them are stack based languages. But if you program in Java, or if you program in C#, you really don't think at all about the stack foundation upon which you are running -- and that's a really good thing! You want to follow the same pattern. A. Realize what basic mechanisms / tools you need, B. Build the tools you need, C. Build your application with the tools you built. You may have to translate your own infix pseudocode to the postfix VM you've created. Do you need Object Orientation?--You can build it with Forth. Do you need multiprocessing?--You can build it. Do you need an Erlang kind of light multithreading?--You can build it. Do you need a Basic, a Pascal, a C#, a Java, a Lua?--You can build it. Build your Roguelike game in your favorite language, then perhaps a different language, then assembly language. Then build it in Forth.
6: At this link, there is a way to make a microprocessor that natively runs CIL (Common Intermediate Language -- the stack based language of both .NET and Mono, which used to be MSIL Microsoft Intermediate Language, before Microsoft Open Sourced the specification). You buy the IP logic block and then program it into an FPGA. Here is the Abstract of a paper that describes the object-oriented stack-based language and implementation of CIL:
Embedded systems and their applications are becoming ubiquitous and
transparent. Nowadays, the designers need to implement both hardware
and software as fast as they can to face the competition. Hence tools
and IPs became an important factor of the equation. In this paper, we
present a synthesizable core similar to the microarchitecture of
Tanenbaum's (2006) JVM processor. The core is an implementation of a
subset of Microsoft's CIL (Common Intermediate Language). We seek to
accelerate the development of embedded software by providing a
platform onto which the whole .NET framework (C#, Visual Basic.NET...)
(along with its object-oriented approach) could execute. We used a
Xilinx Virtex II Pro as the prototyping platform.
7: Go to the current work-place of Charles Moore, the father of Forth, GreenArrays, Inc. and look under Features for "Implements the colorForth instruction set", -- and you will find that he, too, has taken his virtual machine, having optimized Forth his entire life, and reduced it to an insanely fast 144 core microchip with a claimed capability of 100 BIPS. Here, you should be able to look at the "colorForth instruction set" and the description of it -- he has removed any fluff and bloat, and reduced it to an extremely spartan instruction set. We should learn from this genius before it is too late (he is advanced in years, and Covid19 currently threatens many of our patriarchs).
Below, I try to more directly handle each aspect of your question:
How would one code an application in Forth (or Factor)?
Same way as you would with any other application, learn the building blocks, and build the simplest thing that could possibly work, then grow it from there.
I'm potentially interested in exploring a stack-based language like Forth (or Factor).
There are a multitude of stack-based languages around. They seem to be the foundation, not only of most processors, but also of most virtual machines, as in Java and the JVM, and C# and the CIL.
What I'd like to see is how an application might be built from the ground up, step by step.
That's a great idea for a Forth book... Anybody game? I know there are a lot of Forth people out there, and because of Covid19, a lot of you are at home, too. What kink of application would you like to see? Just looking at FPC teaches a lot.
The tutorials I've found are rudimentary and are not helping me to understand the bigger picture.
There are higher level tutorials out there. But widen your search -- include JVM, CIL, and even LUA (because I think it has a VM, too). Write an app in Lisp. Then take the primitives you built in Lisp, and implement them in Forth, or Factor, or CIL, or JVM instructions.
It's confusing to think of how one might manage the stack when dealing with lots of parts.
That's why I said that you should learn an assembly language -- because most stack-based languages are a micro-step up from that. You have to learn the basic levers, springs, latches, and other primitive mechanisms out of which all of our software is ultimately made. But you only think in terms of stacks to make the primitive mechanisms -- once you have those made, in general, don't even touch the stack stuff -- think only in terms of the basic mechanisms, then build progressively higher layers, even progressing to object orientation, as exemplified in the CIL and JVM. The better applications are layers of implicit DSL's, each DSL targeted at a step up from the previous one. The layers are: Assembly-Language, CIL or other VM, BIOS, Operating-System, Library, Business-Language, Application. Most people only think of the Business-Language layer as a DSL, but every single layer is its own DSL, and really, every class, method, object, config-file, and specialized language, like HTML, CSS, JavaScript, etc. -- they are ALL DSL's, either explicitly (formally specified) or implicitly (created by the programmer as things are built.) Understanding gained from book "Code Complete" second edition -- read over and over is my suggestion.
I've always thought (maybe wrongly) that a good way to learn
a language would be to use it to write a Roguelike game.
Sure... but pick anything you like, really. But perhaps try getting an Arm-based Arduino, programming it, disassembling that, then writing your own assembly language -- then get a Forth for that Arm chip, and program it in that. Then implement your Roguelike game in the Arm-Forth.
I'm having trouble trying figure out how one would juggle a lot of
things on a stack: a maze, dozens of creatures, treasures, character
stats, etc.
Build your "Rogue" Domain-Specific-Language, make that into a VM, then implement the VM instructions first in a high level stack language, like CIL, then try to figure out how to do it in one of the low-level stack-languages. There are many flavors of object-orientation implemented in Forth -- spelunk the old Forth Dimensions articles
and some of the old Forth conference presentations to find them. Google, and the "Internet Archive", or Way-Back Machine, are your friends for this.