I think I might try replacing the hardware before I give up and replace
the entire door. (Heck, for a while now I've been using some jimmied-up
screw and washer to make it work.

If by "door" you mean the actual wood door, you shouldn't need to replace
that, unless it's badly damaged. '

If by "door" you mean "the entire hardware kit" then disregard this g.

-Tim