It will be interesting, I have tried that, and never gotten it to work, but usually I am doing it because the batteries are dead or weak anyway.
A couple thoughts, I was told never put in a bigger battery than what is called for, because it will burn the starter up faster, Also even though you have powered the fuel pump solenoid from a seperate source and you will probably hear it click on, the engine still has to turn over at a minimum of 100 rpm. Obviously it tought to hear the difference between 150 and 50 rpm.
Last spring we were out in my Suburban, stopped at a gas station for a Soda, when I came out a guys stops me and asks if I know anything about the 6.2's. He had the same problem you describe. Hot spring day, melting the snow off. He was towing a trailer, just shut it off while the wife and kids ran to the restroom. 15min later no start.
He cranked it over, and it sounded like it cranked fine, but when I shut mine off and restarted it, you could hear the difference, it was dramatic. He was suprised since his starter was "new"
He looked at me funny when I put snow on the injector pump and starter until I got them cool to the touch. He hopped in and it popped right off.
That is the main reason I try not to shut mine off, they will keep running, if you can get them started.