Try re-soldering main fuel pump relay.. It's done by Mitsuba and is all wrong..so when hot it can do than..
Since you posted in November, my replay is out of question unless you are from warm country.
I got the same problem on 27.11.2011. it won't start, but i steel didn't checked all that you did cause i thought my relay is finally dead cause it gave me some troubles..I'll try all you did in next few days..
If you solve problem please post solution.
We have one more guy that has exactly the same problem and symptoms, on same day as me:
http://youtu.be/0K-70RNi8GI
Guess all Integras are programed to be doomed til 2012.
just kidding.
If you find out anything be aware that there is lot of us with same problem, so pls replay with solution.