If it is grungy, it goes for cheap, and I have the patience to overhaul, clean and refit fine old machines.
I always see the opposite, some piece of crap with cheap Suntour parts rusted frozen that the guy wants $500 for. Personally, my dream find is an old Raleigh or other Brit-make 3-speed Tourist style.
Oh, those are common here. It is quite easy to find Raleigh Sports, and other 3 speeds cheap here. I must have 8 Sturmey Archer hubsets, and know of three machines in great shape that are quite cheap. Blue Heron Bicycles on E13th St specializes in old bikes and has several upstairs in the loft, and Revolution used bicycle Shop on Blair Blvd has some of those and some more rare three speeds.
I guess I am spoiled because this city has five percent of commuters going to work on bicycles, and a long history of deep bicycle empathy and use. It's the main reason I stay here, I've ridden in metro areas where I felt I deserved combat pay the road system and bike situation was so horrible.
I only have one myself, a Puch with Austrian rear hub I came across abandoned because of a blown tire in the Burnside District of Portland. I brought it home and use it if I am just going around the immediate area. It is bulletproof, and thieves don't covet it.
As for your shifting problem, there are screw on cable stops and barcons (at the end of the handlebars plug style shifters) that would give you more convenient shifting. I would use SIS cable and housing though, as that setup is longer, and longer means stretching.
Ratchet barcons are popular and show up often on E bay. I have a couple of sets of those too as I try to upgrate to SIS barcons on my touring bikes.