We towed a ~6700-7000 lb. (loaded) toy hauler with ~1000 lbs. of tonque weight (plus 400 lbs. of passengers and gear) with a '12 Tundra double cab 5.7 2WD during several cross-country trips.  FWIW, these numbers are CAT scaled--not guess-timations based on empty/GVWR factory numbers.
Don't believe the drivetrain (engine, tranny, etc.), frame, or suspension has changed on the 2014-2016 Tundras vs. the 2007-2013's (exception minor tuning to the rack & pinion and shocks).  Door jam sticker payload rating for the above truck was 1460 lbs.  I'd check the door jam sticker on a similarly equipped 2016 on the lot before putting much faith in the salesman's estimate of 1680 lbs. 
Anywhoser, the 5.7 has more than enough power to handle 7 percent grades at 60 MPH.  May have to downshift to 4th (~3k RPM), sometimes 3rd (~4k RPM's).  Not a problem unless the sound bothers you.  This is a 32 valve DOHC engine, so it does loves to rev.
Fuel economy was approx. 9.5 MPG at 55 MPH.  Dropped down to 8.5 MPG at 60-65 MPH.
As for payload, that's another story.  With 1400 lbs. of payload (tongue weight, passengers, and gear) and properly adjusted 1000 lb. WDH, it would go down a smooth road just fine.  However, throw in some rough expansion joints like the ones they have on I10 in Louisiana, well things went from fine to jarring.  You could feel the rubber axle stop contacting the frame on every bump.  Not much suspension travel remaining when these trucks get close to their max payload.  The Tundra's rear suspension has approx. 3 1/2" of travel when empty.  This drops to approx. 1" when loaded to maximum payload.
Funny, you're thinking about downsizing.  I just traded in my '12 Tundra for a new Ram 3500 just because of the payload issue.  Yes, the Tundra "handled it", but I got tired of living on the edge.  Plus, we have plans to get a larger toy hauler.  It gets tiresome having your future choices limited because of tongue weight.  Would much rather concentrate on living comfort, features, etc.