I need suggestions for a 2001 Honda Accord EX V6 stalling issue!

Hello,

After going to several mechanics with no diagnosis I am in need of some help. My engine is stalling while driving, when accelerating out of an idle position, occasionally in park (rare) and when it is being started up in extreme heat after sitting for several hours. In all occurrences the engine will crank, but wont turn over immediately. I've found that in extreme heat it can take up to an hour to finally catch. The lights are coming on. The driving while stalling is the biggest issue.  The best way to describe it is the car reacts similar to running out of gas. Ex. I was going 60mph last night when the accelerator stop responding. Power steering goes out. As I came to a stop the engine quietly cut off and the lights came on. The engine immediately turned over and I was on my way again. When sitting in extreme heat the engine turns over and immediately stalls. In these occurrences it can take awhile to turn over, but once it does, it generally will not stall again while I drive it home or go out again later.

I have replaced both the ignition switch and the IACV valve. The idle is still a bit rough when I start the engine up cold. Like there is a bit of a hiccup in the rotation. It is irregular. Apparently nobody can get it to duplicate these issues. It has happened to me 5 times this week. Once while driving, twice coming out of work where the car had been sitting in the sun all day, and once pulling out of a convenience store. I'm at a lost, and need help. I'm considering replacing the main fuel relay, but when I suggest it the mechanics I've spoken to seem to think that isn't the issue.

There is no check engine light. This has been going on erratically for nearly 6 months. If anybody can point me in the right direction it would be appreciated.