Great engine, crappy transmission.
The problem with the transmission, particularly in an E-350/450, is the stock transmission can not flow the oil through it fast enough to keep from getting toasted. No matter how large the transmission cooler is, the passages inside the transmission are so small that the oil gets cooked before it can get through to the cooler. The added vibration and shocking from the diesel combustion cycle doesn't do the transmission much good either.
Plan on replacing the transmission at some point. When you do, you need to spend the $$$$ to get one that has the upgrades and work arounds that will allow the transmission to go the distance.
15-years ago when I was operating three Ford E-350 chassis buses with the 7.3L engines I put in seven transmission in those three buses over a period of about three years. The furthest I got with any of them was 42,000 miles and the least was a little more than 12,000 miles. Each of them got regular maintenance but had multiple drivers so it was hard for my transmission guy to figure out what, besides the built in design flaws/compromises, was causing me to have such bad luck with the E4OD transmissions.
Fast forward to 2016, there are now several companies that specialize in remanufacturing the E4OD and doing the work arounds Ford wouldn't do (if they did they most probably would have been on the hook for $$$$$$$$$ to repair and reimburse people like me).
Companies like this one: Legendary E4OD Heavy Duty Diesel Transmission
Good luck and happy trails!