The boot menu uses some form of bank switching to get to the actual game ROMs and their specific switching strategy, if any. The 2600+ and 7800+ would need to know the method (a write to a specific address, perhaps) to get to the specific part of the ROM on a bank-switched game anyway.
I never tried that, so I might be very wrong in my assumptions.
In the case of the imaginary cartridge with the UI, changing the ROM that’s mapped to the cartridge space with the physical UI and resetting the console without resetting the card controller should do the trick.
The bank switching mechanisms in all commercially released games can be enumerated and emulated by the 2600+, but I think they just haven't gotten around to updating the firmware. Many bank-switched commercial games still don't work afaik.
Flashcarts are more of a crapshoot. They use unknown bank switching mechanisms and Atari does not want to support their use.
> In the case of the imaginary cartridge with the UI...
Not so imaginary! This is what the pack-in cart that comes with the 2600+ does, there are DIP switches for game selection on the cart itself. I don't know of any flashcarts that do even this, let alone something more sophisticated with buttons and an LCD readout like a Gotek drive emulator or something. Would be nice though...
I never tried that, so I might be very wrong in my assumptions.
In the case of the imaginary cartridge with the UI, changing the ROM that’s mapped to the cartridge space with the physical UI and resetting the console without resetting the card controller should do the trick.