did the vet do a fecal test on him??
All of the above could certainly contribute to diarhea..
I guess first, tho the food is lousy, I wouldn't switch him just yet. Exercise can cause some stress sometimes, is he drinking alot of water?
He can also become dehydrated from excessive diarhea..
What I would do, have a fecal run, and I'd fast him for 24 hours, OR if you are going to feed him, try some boiled chicken / brown rice, and yes the canned pumpkin..
I don't like to give my dogs anything like Immodium AD (tho some suggest) only because if they have 'something', I want them to rid their system of it ..
Lepto shots are notorious for making dogs sick..not sure if it would be just diarhea tho...
The tons of treats could have upset his gut as well..I'd start with a fecal..Hope he feels better soon, he is a handsome dude