BREAKTHROUGH.
@derekb: I noticed after looking at your photos that both of your MMC chips had a larger font, while all the carts I made had a smaller font, despite the same MMC revision numbers. The one cart I managed to just get working had a larger font as well. So then, what would happen if I removed the smaller font MMC from an NTRQ cart that didn't work and replaced it with a large font MMC from a completely different mapper/cart?
NTRQ now works on an NES Open Golf cart with the new large font MMC, despite being the same exact revision.
So after poking around bootgods site, I see that (according to the photos) the smaller font MMC chips are manufactured by NEC:
http://bootgod.dyndns.org:7777/profile.php?id=179
http://bootgod.dyndns.org:7777/profile.php?id=472
while the larger font MMC chips are manufactured by Sharp:
http://bootgod.dyndns.org:7777/profile.php?id=700
http://bootgod.dyndns.org:7777/profile.php?id=519
This is a little misleading however, because the photo/info on bootgod's site shows that NES Open Golf had an MMC manufactured by Sharp (large font) while any copy I have in my possession has an NEC MMC (small font). It also states Zelda had an NEC MMC as well:
http://bootgod.dyndns.org:7777/profile.php?id=703
http://bootgod.dyndns.org:7777/profile.php?id=173
So, having figured this out, it would seem as though it's luck of the draw when purchasing SNROM games. It's probably best to have a few spare Sharp MMC chips laying around if anyone is hardcore enough about not wanting to use Powerpak.
NOW the question is this: What is so different about the Sharp/NEC MMC chips that one works and one doesn't, despite having the same revision number? Furthermore, why is it that you can get an NEC MMC to work when using the power-switch-toggle-while-cart-is-in-the-NES-but-not-actually-pressed-down trick?
Perhaps you can short a pin to get it to work, instead of replacing the MMC outright?