I think that if you remove the phrase "that are utilizing 3rd party controls that I have no prior experience with", you might have a better description of your larger problem.
If "Agile" has taught us anything, it's that, if management expects you, on an ongoing basis, to estimate projects that way, and you will "look bad" if you say it can't be provided because you don't have enough information, you're on the highway to FAIL.
The biggest problem is going to be the issues that you have no control over, and which you haven't even identified yet. How often have you looked back and said to yourself "Well, I hit my estimate right on the button - on the third try, after I figured out that ... and that I needed version ... and that the dba would be on vacation for a week and that the Project Manager would need me for ... for a week and that my wife was pregnant and ...".
I'd try real hard to say, "I can identify the critical risk factors and come up with a checklist of deliverables to test them in xx days. At that point I'll give you another incremental estimate."
And it would be real nice if you could suggest that they should "Please insist that I never try to give you a credible estimate of that type in the future. Fire me if I try."
(Overstated, but only slightly.)