Probably a pretty good match for that trailer, as long as the payload numbers are right.
You'll probably solve the frequent shifting issue. But not sure the mpg is going to be much better. Towing, at least. (I'll probably be lots better unloaded).
2008 Hornet Hideout 27B
2010 Chevy Suburban 1500 LT, Z71 package, 5.3/6A/3.42
2015 Ford F150 XLT Supercrew, 2.7 Ecoboost/6A/3.55 LS
Prior TVs:
2011 Ford F150 Ecoboost 3.5
2006 Chevy Silverado 2500HD Duramax LBZ
2005 Chevy Suburban 1500 4x4 LT, 5.3/4A/4.10