I'm having the same Cavern Fighter issue with the Gen 2 Phoenix also.
It works fine on the stock Colecovision. (This is a really fun game.)
If you have a Snes NTT controller and use that instead of using the Colecovision controller ports you can still play the game on the Phoenix.
The game will still automatically start though.
The first time you press a button the auto fire will stop and you can play like normal.
Once the game ends you can access the title screen normally.
If I use a stock colecovision controller the game will crash and reset.
Interestingly enough if you don't have any controllers plugged in the game still auto starts with the auto fire.
On a side note with the Gen 2 Phoenix,
I noticed the A E rom also starts the game with an auto fire. Once you press a button the auto fire will stop and you can play normally.