You can also replace the socket on the NES itself for relatively little, it took me about 20 minutes a couple of years ago and it made it much more reliable.
You can also put the 72 pin connector in boiling water for like 30 mins, take it out and let it cool. That should reset the pins back to "factory condition"
If your socket is the unreliable part, I've found that getting a game fairly wet on the contacts with isopropyl alcohol and then repeatedly inserting/removing it will get the slot nice and clean inside. I usually blow it out with compressed air after that.
I’d like to add a different take to this. I have contacted Valve support in the past, clearly stated my problem, and got a response that looked like they read half of my question and responded without reading the entire thing. If the same team that responds to their customer support reads this stuff, which seems crazy, they didn’t bother to understand the problem before responding.