Here is a way to run ROM cartridges on a V2.2 console. Plug in the cartridge, then go to TI BASIC (your only choice) and run the attached program. There is embedded code in this so cut and paste will not work. This is a simple assembly program that uses the playground loader. It sets the VDP registers to the values used at the cartridge menu screen, then looks into the cartridge, finds the startup address of the first program in the list and runs the code. This has been tested on Classic99 and seems to work. It's a good first step - it could benefit from a fancier menu, especially if there is more than one option in the cartridge.
Silly graphic kept stealing my mouse.