Hello!
First of all, since I don't know specific details of this game, I don't know how much of it will be possible without remaking the whole game. Also, how long it'll take.
However, I've studied deeply the Gameboy Color console, which is extremly similar to the NES. I also program in assembly. I even attempted to program a game for GBC, but I failed due lacking proper programming tools, logic programming knowledge and game programming knowledge. I was just a teenager in highschool. Today I have a degree in IT with a final project about a digital signal processing "software" done in Mathlab (so, python programming pretty much, despite you really don't make a proper software in Mathlab per se) and a I have taken a game programming course.
So the likelyhood of being sucessful for your project is huge, specially given my huge interest (and dream, despite the failure) of making such project.
I've charged the value of 700 for 30 days (777.78 due Freelancer.com fees), which is my needed monthly income. I don't know if the porting will take more than a month, but this is likely. But I'm willing to work in a full-time like fashion for this project. And while I don't have experience in this, I'm someone who actually read circuit schematics of a GBC.
I hope I can be within your budget.