Tim,
> The listening position for the HT will be just about dead center in the room <
If by "dead center" you mean halfway front to back, that's a big mistake. Much better is to be about 38 percent of the way into the room from either the front or rear wall. With a 19 foot length that distance is about 7'3". For nearfield monitoring being 38 percent back from the front wall is best. In a home theater setting with a large screen TV you'll probably be closer to the rear wall than to the front wall.
> doors in both corners of the front wall - the doors in front make it impossible to put bass traps in those two corners. <
Not so! You can put two bass traps adjacent in those corners - one on the wall and one right on the door. There are also corners where the walls meet the ceiling and even where the walls meet the floor. Those are every bit as valid as corners where two walls meet.
> I have also attached a screenshot from ModeCalc <
I recently made a new native Windows version of my ModeCalc program that looks nicer and also gives more information and with a more detailed Help file. Here's the link:
www.realtraps.com/modecalc.htm
> Note the humongous node at 76Hz. <
All rooms have peaks and nulls. Which proves the point that you need as much bass trapping as you can possibly manage. You'll never get that room perfectly flat, but you can definitely get it from "This sucks" to "Wow, this is great!"
> Can I do this with some 703 straddling the corners, or will I need to build something more elaborate like a membrane trap or Helmholz resonator? <
Yes, 703 or equivalent can make a big improvement. I'm not a fan of tuned absorption, though both of those trap types can be made more or less broadband to cover a range of about an octave. In a room that size you can do a fine job with porous absorbers.
> Does anybody have any thoughts on a good RT60 target for a multi-use room like this? I'd like to get an idea so I know how much 703 I should buy. <
Maybe 200 to 300 milliseconds. But that's for
all frequencies, not just 1 KHz!
--Ethan