My Sprinter was the same way, when I had the exhaust replaced the shop rerouted the pipe straight out the side, but honestly had no fumes in the cabin.That has concerned me as well- wasn't sure if all Transits were that way or just the extended length ones.
Glad you found your problem and it was an easy fix.
I like the idea of throwing a carbon monoxide detector to check the integrity of the exhaust. My sister complained of fumes in the back seat of my '66 300. I am just looking for an excuse to add dual exhaust.