Due to spending $140 on the new remote, I just want to stay away from messing with the internals.

Why push buttons when you can just close contacts? Buttons eventually fail and solenoids, while mechanically cool, are noisy. Break the contacts of the button out into two leads, and then close them via any method appropriate to the task - transistor, relay, optocoupler, or any others.

I have a remote for an adjustable mattress that is no longer functional due to me being overzealous. The remote is expensive ($100+). I attempted to hook up a logic analyzer, with no experience of course, and I damaged the copper runs. So from here, I want to try to go mechanical.

Has anyone seen a project of a few solenoids to push a few buttons?

I found this https://www.reddit.com/r/maker/comments/95wfz2/i_built_a_midi_player_piano_with_solenoids_3d/, but it's a bit to the left of what I'm looking for.

Button Pressing Machine?