Your use of passive voice suggests it wasn't you that messed this up.
Here's the specs for the VRC1 used in this game:https://wiki.nesdev.com/w/index.php/INES_Mapper_075
and the much more common MMC1 used in the prototype:https://wiki.nesdev.com/w/index.php/INES_Mapper_001
One thing to notice is that the VRC1 has a maximum PRG size of 128KB, so maybe that's what went wrong. The MMC1 can go up to half a meg. The CHR works the same in both. A key difference is the granularity of the banks: although VRC1 can only do 128KB in total, the banks are 8KB rather than 16KB, so the game may use them differently than an MMC1 game. Then again, as you said the prototype used MMC1, perhaps it didn't take advantage of the granularity and therefore a switch would be easy.
The big problem is how the two mappers switch banks. The VRC1 works like most other mappers: just write the number of the bank you want to the address you want to put it, and bam, done. The MMC1 works quite differently, as the NESdev page shows. However, having that prototype will be very useful, as someone can compare the original with the prototype and see how the internal processes differ. I could have a look to see how it works, but I can't promise anything.
Anyone else with experience of the MMC1 might want to chime in here. On second thoughts, using the UNROM mapper instead might be a better choice, since it seems to work quite similarly to the VRC1, but has double the PRG capacity:https://wiki.nesdev.com/w/index.php/INES_Mapper_002
If the bank switching works the same, it could be a very simple swap. But the problem in any mapper hack is how to tell the game to switch banks: like, how does the game know that THIS bit of dialogue is in a particular bank? That can be a challenge.
EDIT: the GoodNES set includes a mapper hack: Jajamaru Ninpou Chou (J) [hM04].nes. It changes the mapper to MMC3. Perhaps adapting the translation to that would be easiest?
EDIT2: Crikey, Taro's Quest is remarkably different to the original. Maybe it won't be so helpful to compare...