Oh duhhh, I linked the wrong thing earlier.
This looks more like it:
http://www.nesworld.com/fakechiller.php
Do these images look like the back side of your PCB, marked Color Dreams or AGCI? The earlier PCB shot I linked, with the little bit sticking out at the top, seems to be common. It might be the original and this is a boot, or just an alternate.
Sounds like your guess might be accurate. I'm wondering why you didn't find the resistor in the case...does the game or the case shell look tampered with? It's not really critical, but would be nice to know.
Replacing the transistor shouldn't hurt anything, but it would be good to get the right value the first time, and I can't see the transistor in your comparison pic well enough since it's so small. Searching for NES Chiller PCB or even "Color Dreams" PCB images didn't bring up better photos, other than that NES World shot which just shows the back of what might be the same PCB.
If you do lock in that it's a Color Dreams / AGCI PCB, here are some places you could try asking:
NES World (the author of that article above should still have the game, I'd hope)
Infinite NES Lives (they manufacture new PCBs and mappers for the NES)
Nintendo Age
NESdev Forums