2007 Tundra 5.7 L

160,000 miles

This truck starts perfect in the morning (extreme heat or cold) or after its been sitting for at least 4 hours.
If started within that average 4 hour period it cranks for an extended period of time, turn it off and start again and then it'll start but sputters and smells like fuel after it has started.
In high hopes of fixing this we have replaced the fuel pump, fuel pressure regulator, injectors, spark plugs, and coils.  Also cleaned the MAF. 

The other issue...... When starting the truck it will turn off so we disconnect the battery and it'll start and stay running.  We switched keys and the problem kind of went away for a while but now it has the issue again.

We would love some help before we get Toyota to pick it apart.  Maybe these problems are related?