Tell me about your angled keys. This is the first I've seen them like this. What are they called?

Take apart any old switch mode power brick, rip off the transformer and unwind the enameled copper wire. Use an Xacto knife to carefully and completely remove the enamel from the entire circumference and test if it wets with solder in 360° before adding it as a replacement.

For my own etched designs that need mechanically solid through holes and for repairs/mods where I need to make a soldering contact, I keep a set of brass micro rivets. The smallest ones I have are 0.9mm and work great with a 1mm hole in the PCB. If you've never seen or tried this, no special tools are needed. Place the rivet in the hole and use a pointy object like a dental pick to expand the back side.

Do you otherwise have no spare pins? Also you can do communication between halves with only a single pin, what protocol are you using?

The other thought is, does the LCD use i2c and are you using i2c between halves too? If so, does the LCD modules have a way to change their i2c address so they don't conflict? If so you should theoretically be able to have all of it share the same bus (the same 2 pins).

At least it's usable. My last pcb I screwed up the gaetreon holes completely. Why do they make key switches so obnoxious.