"Is there any low-output reasonably low cost point-of-use water
re-heaters that migth solve the OPs problem? Something that could raise

the temp a few degrees for just a single faucet. "

I've never seen one. I think the problem boils down to this. Someone
earleir pointed out that a reasonable estimate of the water in the
pipes could be a half gallon for the 10 seconds or so it takes to make
its way through the pipe. So, raising a half gallon of water from say
55 degree basement temp to say 120 or so in 10 seconds is on the order
of what kind of heater you would need. Think about how long even a big
240V burner on an electric stove takes to do that and it doesn't sound
practical.