I have a 2GM20F in my H290, and at cruising RPM (~2300) it burns a little less than half a gallon of fuel per hour.
The numbers: With the boat (14k lbs), heavily loaded (add 3k lbs), crossing the Gulf of Mexico (no current to speak of) in NO wind (thus no sailing or motorsailing), we calculated the burn rate at .42 Gallons/hr with an average speed of 5.5 knots.
You, of course, will need to factor the current working against you for the majority of the trip. The 'gallons per hour' won't change much, but the 'miles per gallon' and 'miles per hour' certainly will.
Good luck with your trip! I'll be headed along that stretch in the other direction sometime next year, as part of the Great Loop. I'm looking forward to spending some time there.