jr,
YES, those single handle Faucets can transfer pressure across the lines !
Given you have your own system, I can't help but think it's a stoppage in the outgoing line from the heater.
As a last resort you could Back-flush, and this is the easiest way I know to do that.
Shut cold supply off to Heater.
Connect a standard Garden Hose to the Drain Valve, and run it outside somewhere.
Open the Heater drain Valve.
Go to any Sink, the further away the better.
Make a "Jumper/connector" pipe, from your Cold to Hot Valve under the Sink. That'd be a copper line about 24" long, with appropriate fittings for the supply line Valves. (Compression/Flare)
Turn off both sink valves, disconnect the supply lines for that sink, and connect the jumper pipe/tubing on the Valves.
Turn both hot and cold Sink valves on, and let it run for about five minutes.
That should reverse the cold water back into the hot pipe, flushing any debris back into the Heater, and hopefully out the drain.
All Faucets should be off during flush.
During the Flush, it wouldn't hurt to tap the Hot Water piping near the Heater, with the handle of a Hammer, not to hard, just enough to give it a good shock/rattle.
I know this is kind of a chore, but, it's the only way I know of to get it done, without starting to replace pipe, or running some De-Scaler through the system.
Have a good Day !
S.W.