Are you saying the belt was replaced recently, therefore you haven't even checked it and automatically eliminated it as a possible cause?
Are you saying the belt was replaced recently and you checked it and it still looks brand new with no signs of damage or glazing?
There is a big difference, and something can go wrong installing a belt. I installed a new belt on my Daughters Cherokee, and she complained of a strong burning rubber smell, the belt tearing apart with little chunks of it being throw all over the engine compartment. So if you haven't double checked the new belt is still good, do it.
As well, I'm puzzled at your Dealer, I can understand if you brought the vehicle to have trans fluid level checked, he wasn't going to start a 2nd job without a work order. BUT, if you describe a strong burning rubber smell, so strong it is nauseating in the passenger compartment, and his reply to you is; "good luck"?
You have to look over the entire engine and exhaust for any evidence of burning or leaking fluids on hot parts of the exhaust and engine. This could be a fire hazard, if the smell is as strong as you say. Look over all the wiring is visible, shorts will burn the wiring.