Downgrading GPU to a model with lower capability and memory for testing

I am developing software that should be running on several CUDA GPUs of varying amount of memory and compute capability. It happened to me more than once that customers would report a reproducible problem on their GPU that I couldn't reproduce on my machine. Maybe because I have 8 GB GPU memory and they have 4 GB, maybe because compute capability 3.0 rather than 2.0, things like that.

Thus the question: can I temporarily "downgrade" my GPU so that it would pretend to be a lesser model, with smaller amount of memory and/or with less advanced compute capability?