Comment re SAS only:

A logit-normal assumption is easily addressed in GLIMMIX and, with a little more effort, NLMIXED.  Also MCMC.  At least as of a couple years ago or so, SAS didn't have an easy way of fitting a binomial-gamma mixture in a likelihood setting.  But see

• Nelson KP, SR Lipsitz, GM Fitzmaurice, J Ibrahim, M Parzen and R Strawderman. 2006. Use of the probability integral transformation to fit nonlinear mixed-effects models with nonnormal random effects. J Computational Graphical Statistics 15: 39-57.
• NLMIXED and MCMC code for fitting both models may in principal be obtained by eliminating zero-inflation terms from code at http://www.umesc.usgs.gov/staff/bios/bgray/code/zibsas.html
  

Thanks for pointing me to SAS and the paper. It's probably not as simple/common as I thought. Also there's the hglm package in R, which seems to enable gamma-distributed random effects, but I'm not sure what "h-likelihood" means and whether it could be used to compare models with different random effect distribution. So, may be I'll have to purchase a new license for SAS. Best regards,