I find that after a couple of hundred miles that a quick stop to fill up the bike's tank, and empty out mine, is a good thing. It allows me to stretch, and revives me for the next couple of hundred miles. I'm not sure that I would want to go 350+ miles between breaks.
For 1,000 miles, starting with a full tank, I would have 4 fuel stops. With 10+ gallons, it would be 2 stops. This would save about 20 minutes on a 16-17 hour trip, but leave one more worn out because of the lack of breaks. IMHO, not only not worth it, but potentially more dangerous.