It's not the end of the world that the controller is the only way to get at the fast forward and rewind buttons. I'm a fairly dab hand with an iron, so I gutted the controller, charted out what pins on the control chip do what, stuck it on perfboard with some Wago-style spring terminals to make running out to other buttons easy, and got out some small wire and the 60/40.

Don't forget the intrinsic documentation. The next poor asshole working on it will thank you, and it's likely to be you anyway.

With a little testing I've now got easy access to run the most important buttons remotely without worrying about tearing the gossamer thin traces from this cheapie single-sided remote control board. Also I added connections to run it from a 3vdc wall wart so batteries in the remote aren't of concern.