Those Aeolian brass threaded Theme valve tops, that screw into threads
in the wood block, impressed me as a great design when I rebuilt my
Duo-Art some 35 years ago.  Mine unscrewed easily, and went back in
without a hitch.  Now, the greatest danger in reinstalling them is that
you will start a little crooked and cross-thread the wood.  If so, the
valve cover will not be square to the valve pad and will not seal
properly on operation.

How can you tell when you've gotten a bad start and are cross-threading
it?  By how hard it is to keep screwing it in.

Since yours were very stiff coming out, it will be hard for you to tell
if you've started to cross-thread.  So it's dangerous to reinstall the
valves until you ease the thread somehow.  Lubricating the brass with
beeswax or (horrors!) silicone might help.

If that fails, your idea of finding the right tap for the wooden holes
and refreshing the thread is a good one.  But -- such a large tap is
expensive, and for Pete's sake, don't cross-thread it!  Actually, most
taps are tapered, so they go in easily at first, giving you a chance to
line it up with the existing threads.  So go for it, if needed.

Best wishes, Mike Knudsen