Bayesian error-in-variables (total least squares) model in R using MCMCglmm

Question

I am fitting some Bayesian linear mixed models using the MCMCglmm package in R. My data includes predictors that are measured with error. I'd therefore like to build a model that takes this into account. My understanding is that a basic mixed effects model in MCMCglmm will minimize error only for the response variable (as in ols regression). In other words, vertical errors will be minimized. I'd like to minimize errors orthogonal to the regression line/plane/hyperplane.

1. Is it possible to fit an error-in-variables (aka total least squares) model using MCMCglmm or would I have to use JAGS/STAN to do this?
2. Is it possible to do this with multiple predictors in the same model (I have some models with 3 or 4 predictors, each measured with error)?
3. If it is possible, how would I specify the model?

I've included a data set below, with a random variable height that is measured with error to illustrate a basic set up with MCMCglmm.

library(nlme)
library(MCMCglmm)

data(Orthodont)

set.seed(1234)

Orthodont$height <- c(rnorm(54, 170, 10), rnorm(54, 150, 10))

prior1 <- list(
    B = list(mu = rep(0, 3), V = diag(1e+08, 3)), 
    G = list(G1 = list(V = 1, nu = 1, alpha.mu = 0, alpha.V = 1000)), 
    R = list(V = 1, nu = 0.002)
)

model1 <- MCMCglmm(
    fixed = distance ~ height + Sex,   
    random = ~ Subject, 
    rcov = ~ units,
    data = Orthodont, 
    family = "gaussian",  
    prior = prior1,
    nitt = 1.1e+4, 
    thin = 10, 
    burnin = 1e+3,
    verbose = FALSE
)

summary(model1)

Carpogonium