Winnebago likes to install 'check valves' on Cold Inlet and on Hot Outlet on water heaters.
What you have going on is one of those check valves is failing....clogging up/restricting flow.
Then when you open/close Bypass valve you allow cold to hot water flow which is disrupting the the clog in check valve
The HOT Outlet check valve is the common one that causes problems due to the scale/calcium etc from inside of water heater getting into the check valve
Check valve is inside the 'nipple' that is screwed into the Hot Out on water heater (top line)....hot water line connects to that fitting.
Will need to disconnect hot line, then remove the nipple/check valve .
Then you can remove the internals/check valve from nipple and just reuse nipple w/o the internals.
Later on replace with new check valve/nipple OR install a shutoff valve on hot out line (on water heater tank side of where bypass line connects)