Apart from the usual MMC3 registers, there is an Outer Bank register at $8010-$801F which seems to latch the four lowest address bits.
In the CPU address space, the outer bank register simply functions as an additional 16K bank number, so a value of #$05 adds a start address of 0x14000. Of course, the MMC3 bank registers 6 and 7 can be set to access an inner bank address of 0x14000+ as well with values #$0A to #$0F. These values have a special meaning: they are hard-wired to access the last outer bank, regardless of the outer bank register, so an MMC3 bank register value of #0x0A will select a bank starting at 0x3C000 (the start address of outer bank #0x0F) plus 0x14000 (the inner bank start address) = 0x50000. This means in practice that outer banks #$00, #$05, #$0A are 80K in size (because the last 48K are taken from outer bank #$0F), while outer bank #$0F is 128 KiB in size, yielding a total PRG-ROM size of 368 KiB. This is the case for both cartridges.
PPU space mapping is different. The same outer bank register also selects an outer CHR-ROM bank, but its size (for the outer bank register's step size of 5) differs between the two cartridges. In the first pack, the outer CHR bank is 96 KiB (MMC3 bank register values #$00-#$5F are valid) yielding a total CHR-ROM size of 384 KiB, while in the second pack, the outer CHR bank size is 120 KiB (MMC3 bank register values #$00-#$77 are valid) yielding a total CHR-ROM size of 480 KiB. If an MMC3 CHR bank register contains a value higher than #$5F/#$77, then the beginning of the last hard-wired outer PRG-ROM bank is mapped into PPU space! The games do not seem to rely on that feature, but it allows me to determine what the outer CHR bank size actually is. Assuming a fixed number of four outer CHR banks, the outer CHR bank size can then be detected by an emulator by simply looking at the number of 8 KiB CHR-ROM banks in the NES header. I don't know how the board actually manages to derive values of #$60 or #$78 from an outer bank register value of #$05, though.
Attached find PCB images,
Edit: See below.