Right off the bat, the problem is not the pressure release. This only vents pressure should the pressure get too high or temp gets too high. It does not affect outflow to the hot water lines from the hot water heater (not attached to the out-flow line) see: http://theplumbinginfo.com/water-heaters/

If it was the water heater, it would be a constant slow flow, and possibly lower capacity in terms of hot water (ie: a 60gal hot water heater acting like a 40 gal hot water heater). It would also be slow heating of water within the water heater.

This sounds like something constricting as it heats up… after cooling it flows normally till it heats up again.

What type of pipes are in the house? I am almost suspecting old galvanized steel pipes. Copper pipe tends not to get calcium buildup as it ages, I am not certain of PEX, but I do know that old fashioned galvanized pipe does clog up with calcium deposits and most San Diego water can be ‘bounced off the floor’ because of the hardness (calcium and minerals within the water). The flow drops because the deposits expand as they warm up… closing any tight opening. Another possible is the valve itself.. Have you tried the hotwater from any other outlets? Do they have the same response (reduction to a dribble as the water at the tap gets hot)?