No point in reverse engineering one- it'd be more work than to just learn how to do it from scratch. Just learn the basics of PPM radio system and build one of those. From my understanding it is almost as simple as you can get for RF. If you are trying to save money, then no need to go PCM or spread spectrum or anything like that.
https://www.electro-tech-online.com/custompdfs/2009/06/mectn004-1.pdf
Is the radio supposed to be $35? Or is the whole rock crawler+radio supposed to be $35? Because you probably could get the radio to be $35 to produce, but I doubt you could get the whole kit to be that much.
But can you beat this one?
**broken link removed**)
It's not hard to replace the MCU if you know where all the pins go- but you don't know where all the pins go and chances are you won't be able to find out on their multi-layer board without schematics even if you had the board in front of you. Also...don't forget you have to do the same thing with the receiver. You'd have to reverse engineer both. Not worth it especially since you are trying to go for cost, and those guys are usually more feature oriented. You'd have to slice through a lot of the fat to find what you want.
You don't seem to have the proper knowledge to design your own radio system, let alone reverse engineer it (which is harder and more frustrating). You're going to have to learn the material or hire someone who knows it, and in both cases once you know what's going on it would be easier to just design it from scratch.