Thanks for the information.
It sounds to me like the fuel is leaking out of your engine. Wayne recommended the same thing I would have. The fuel pressure regulator is always the most likely cause. It will fix this problem 9 times out of ten.
Since the regulator did not fix it, there are only 2 other reason the fuel can leak out or your 3406E. You either have a plugged or restriction fuel tank vent tube or a bad fuel transfer pump. It easy to check the vent tube. Just blow air threw it. If it is restricted, the supply line will pull a vacuum on the fuel system and suck the fuel out of it.
If your vent line is OK. The problem is your fuel transfer pump. When the engine is shutdown both the regulator and the transfer pump are suppose to hold fuel in the engine.
Basically, the relief valve in your transfer pump is not closing. Slowly over night the fuel is leaking out. The only way to test this is to cap off the fuel inlet port of the transfer pump. If the next morning you reconnect the line and the engine cranks and runs fine, it is the transfer pump.
Most of the time I check the vent, then check the regulator, if they are OK, I replace the transfer pump.
Please let me know if you have any more questions.