Moderators: this thread should be moved to the NES Hardware and Flash Equipment forum.
Random brain dump of information:
I can't tell if you're wanting an English version of Shadowgate on a Famicom cart, or a Japanese version of Shadowgate on a NES cart. It sounds like the former, but I can't tell for sure. I'm going to assume the former, barring info in a couple paragraphs near the end of my post.
uses the HVC-TKROM PCB board type. This is MMC3A (mapper 4) with battery-backed SRAM (WRAM) for save games.
uses the NES-TKROM PCB board type. This is MMC3B (mapper 4) with battery-backed SRAM (WRAM) for save games.
Both the Japanese release and the American release are 128KBytes of PRG, and 128KBytes of CHR. So there are no physical capacity (size) differences. Battery-backed SRAM is 8KBytes as well.
Famicom and NES cartridges do not use EPROMs, they use mask ROMs (for both PRG and CHR). These are read-only ROMs, "internally wired" (manufactured) at the factory with all the bits in a certain pattern. Mask ROMs are not 1:1 pin-compatible with EPROMs. To use EPROMs, you must rewire the entire cartridge. Someone will literally have to tell you "cartridge connector pin N --> PRG pin N" and same for CHR for each and every pin. There may be other adjustments as well, I simply don't know.
MMC3A and MMC3B have no hardware differences except for the IRQ counter (used for split-screen effects). I do not know if Shadowgate uses this feature. Details are https://wiki.nesdev.com/w/index.php/MMC3#Hardware
. You could try it and find out, or reverse-engineer the game to see if it does.
If you were to desolder the NES cartridge mask ROMs and put them on the Famicom board, barring MMC3A vs. MMC3B differences, the game should work. However, you brought up mention of EPROMs, implying you have your own code or something -- possibly a fan translation (because you used the word "translating" in the Subject title, but I can't tell if you mean CONVERTING, or TRANSLATING (as in language)).
That said: if you are going to different Famicom cartridges (i.e. not real Shadowgate ones, but other games/etc.), you're going to need to make sure they're HVC-TKROM, use MMC3A if at all possible, and that they have battery-backed SRAM (WRAM) on them. Anything else you would have to solder + wire up yourself. Here is a list of HVC-TKROM games
(multiple pages) which you could use as "donor carts".
Alternately you could try to find a distributor who can manufacturer Famicom cartridges for you, either with EPROM or flash on them. I don't know who does this right now, other than shady Chinese dealers whose carts may lack proper voltage regulation (NES/Famicom stuff is 5V, not 3.3V like what most hardware today uses).
If you're going the other direction (doing something on NES cartridges, not Famicom cartridges), Infinite NES Lives sells MMC3 NES boards
(not Famicom boards), but the MMC3 boards they sell are not
TKROM (i.e. they do not have battery-backed SRAM on them), so they wouldn't work for Shadowgate. Rather: the game might run/work, but the save functionality would not.
If you have no experience with any of this stuff, and you just want to "get something working", you are probably better off buying a PowerPak or EverDrive N8, sticking with NES ROM files, and getting a NES-Famicom adapter (72-pin-to-60-pin adapter).