There are two issues here: Power supply to the chips, and I/O levels. Power supply is relatively easy, you can use a voltage regulator to produce 3.3V from 5V. The tricky bit is I/O: As far as I understand reading signals output by a 3.3V system is no issue on a 5V system (TTL considers everything over 2V "high"), but a "high" produced by the 5V system is over the limit of the 3.3V system. That MAY work fine, or break after a while.
You can use voltage level shifters, and some official boards actually use them.
As for the tile ROM, it is on the same board as the program ROM and ASIC. The program ROM is a socketed EPROM on the boards I've seen (I guess to allow field updates), the tile ROM is a surface mount chip.
Edit, as an example here is IGS PCB-0468-02 GT-A. Sorry, I noticed some small typos, it was late. Unfortunately I lost some source files in an SSD failure, so I can't easily fix them.