My educated guess is that your board implements CNROM (iNES mapper 3), with the '161 controlling which 8 KiB bank of CHR ROM is visible. With only trace cuts and rewires, in theory you could upgrade it to a subset of GNROM, Color Dreams, or BA-JOGGING.
GNROM (#66)Licensed commercial GNROM games use a 128 KiB PRG ROM and a 32 KiB CHR ROM. The PRG ROM is too large to fit in your 27C512. The cost-reduced MHROM would support
Super Mario Bros./Duck Hunt but that's it.
BA-JOGGING (#3)Bandai made an oversize variant of the CNROM board that supports up to 128 KiB CHR ROM. It was used for
Family Trainer 4: Jogging Race, but that has 128 KiB CHR ROM. A functionally compatible board was also used for Panesian's porn games, but I don't know how big their CHR ROM is.
Color Dreams (#11)A lot of games by Color Dreams use PRG ROM and CHR ROM no bigger than 64 KiB. Games after it pivoted to Wisdom Tree (other than
Bible Adventures) use 128 KiB ROM.
BNROM (#34) or AMROM (#7)The vast majority of BNROM games are 128 KiB (
Deadly Towers) or bigger (
Lizard;
Haunted: Halloween '85). But if you have a 6264 or compatible SRAM, you can rewire the CHR side to take that and then route the D0 output of the '161 to PRG ROM A15. This would give you
240p Test Suite and maybe one revision of
RC Pro-Am if it doesn't rely on ANROM's bus conflict avoidance.
EDIT: Avoid loaded word "clone" for Panesian products