I have the same truck and tow a 11000 5th wheel through t.hr mountains of West Virginia. My gas mileage averages 7 to 8 MPG. I quit looking at the instant mileage it hurts to much but, yes I have seen as low as 3 when pulling a long grade. I read the manual and learned that shifting to M on a 6 speed will only give you 4th gear and no higher. They recommend shifting to M if the tranny is shifting up and down a lot, I haven't had to yet it will down shift fine and yes the RPMs can reach over 3000. SO it seems as if mine is acting the same as yours. I will admit I went from a 1500 5.3 to the 2500 HD and the 2500 is a MUCH louder truck all around.
Scott & Val
2015 Surveyor 293 RLTS