Still, I have noticed that when I start the car first thing in the morning I hear a sloshing sound under the dash.  Doesn't that sound usually indicate air pockets in the heater core, which can account for reduced heater effectiveness?

If there IS air in the core, it is really stuck there, because I would think regular use would have worked it out by now otherwise.  Any thoughts on how to bleed it? 

When the heater is operating - what sort of water flow do you get out of the open return hose?

You might check the heater hose routing.  The hose coming from the intake manifold (supply) goes to the lower connection on the heater core while the hose that connects to the upper heater core connection provides the coolant return back to the water pump.  This helps to purge the air from the heater core and in turn, provide for more heated water to go through the core.  If the hoses are hooked up in reverse, an air pocket remains in the heater core without easy access out.

As Steve mentions, checking the amount of flow going to the heater core is also a great suggestion.

I am going to go ahead and order a replacement for the heater shutoff valve though.  For some reason, I always thought it was a bleed valve and not a water valve, but regardless, mine is so stuck that the fingers you turn it with broke off rather than let the valve turn!  So I'm highly suspicious of a restriction there.  Last resort will be to check for debris in the heater box.  3/8" male pipe thread is the correct thread for that valve into the intake, right?