Ok, so I did some testing and I don't know if it is foolproof, but I might have a solution. I recommend you make a back up folder for each of the models (put those folders elsewhere on your pc so they don't interfere with the testing), just in case the fix doesn't work.
In the model folder of one of the models, change the .vtube.json file name to something different. In my case, I added test to the end of the model name. Don't change any other file name outside of that. The first image shows my file names. ||(My .moc3, etc and my .model3.json files are named slightly different because I had exported my .model3.json with exp3.json files and didn't adhere to my own format, but model still works fine with even that small name difference)|| I recommend closing Vtube Studio before making this change and relaunching the program after.
You should then be able to go to the settings in VTS of the other model (the one you didn't change the .vtube.json file name), and change the model that it changes to in the hotkey settings to the model with the file name changed. The second image shows the difference for me and how the names are different.
Using your hotkey setup, you should now be able to switch between the models without issue.