Improve the data binding between GUI and backing data

[fluffy-critter]

When I first started writing the GUI, I tried making an overly-fancy data binding layer, which ended up being too complicated and fiddly, and I was like, okay, I'll just apply the bindings manually for now and then figure out a better way to do it later.

This has, not unexpectedly, been a bit of a disaster in terms of some wonky bugs, so that'd be a nice thing to fix.