Not sure how structural seam sealer would be. I'd think some welds would be needed. If you're going thru that much trouble/expense, it would be easier to find a new bed. They're out there...just have to look.
Seam sealer is a form of caulking. No structural strength. There is 3M Panel Bonding Adhesive 08115 which if you shop around can be bought for $45 for 200ml and YouTube videos on how to apply it.
But by the time you buy enough of it to do the job and all the new panels needed, both inner and outer, you'll be better off just finding a good bed. Take a vacation in TX or AZ and pick one up.