Originally Posted by
Retro Grouch
If it was my bike, I'd replace the freewheel with a modern one, convert the shifter to friction, and continue to enjoy it for what it is. My bet is otherwise you'll drive yourself crazy trying to make the indexing reliable and you won't be able to enjoy the bike.
Why not replace the freewheel with a modern one, and see how it goes. If it works well, job done. If it does not work well, then consider other things.