Welcome to the forum newfoundlander.
The dry hitch weight on your Springdale is listed as 675 lb.
Dry trailer weight numbers vary between 6235 lbs. & 6257 lbs.
2010 specs here: (shows 6235 lbs)
http://keystone-springdale.com/index...LSSR&year=2010
2010 Brochure: (shows 6257 lbs)
http://www.keystonerv.com/media2/doc...ngdale2010.pdf
Using the truck's towing capacity that you provided [6800-7000], then you are correct... chances are you'll reach that limit quickly with only full LP tanks, battery, & minimal supplies/cargo in the trailer.
We have no experience with the Tundra, but hope the above info helps.
Terri, the Chevy co-pilot