The problem with batching them is that you might end up saving as the improper compression format. Yes, it’s slower if you don’t do it by batch, but well worth on saving the filesize, bandwidth and ultimately the loading times of joining your server.
If only the textures seem to change, then you need to generate MIP maps. If the whole model seems to change, then the issue is with the model lacking LOD versions. Why are you still replacing cars when you can add new cars?
There indeed seems to be a problem if the texture dictionary is over 16MB. If you manage to downscale textures enough and get it under 16MB it will work. I have updated the OP with this information.