work them out with patience.
Works for you also when there's plastic involved?
Use a "sucker pump" to try to get out the solder.
That's mainly what I tried. The result was mostly sucking out the extra solder I added for heat transfer.
I even wasted a bit of my precious Chemtronics wick, to no avail (too bad the fake stuff from eBay does absolutely nothing, at least for me).
just build a new PCB
Not so easy at all, and then, it's back to the core problem of no switches available.
someone with a proper de-soldering station. (I.e. a motorized suction pump with a heated tip.) ... local hacker space or amateur radio club
Could indeed be handy, but there's nothing nearby I know of.
Or, better yet, use this project as an excuse to buy your own! 
It's going to be a very poor excuse. If to clutch at straws, the more dignified thing to do would be to just buy the gear without excuses.
