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Kevin, it sure sounds like you indeed have a faulty valve or two in that bypass system. I’m going to guess they are plastic valves, which seemingly have issues with the constant exposure to the heated water. Somehow, either the plastic body or the valve portion warps over time and either gets stuck in the closed (or partially open) position. I’d toss those plastic valves and install a set of brass valves in their place. I’ll double my wager that all will be well after they are replaced.
There may also be a one-way check valve or backflow preventer positioned at the hot outlet of the water heater. A faulty check valve at the hot outlet could also reduce, minimize or prevent adequate pressure and flow from reaching the hot faucets. Some water heaters have a check valve located at the cold water inlet to the heater, but since you're able to fill the heater and see it draining, a check valve at this location is probably still viable. But like the bypass valves, if those check valves are made of plastic, I'd replace them with brass valves.
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