I have a 2000 F250 7.3L. I bought it at 93,000 miles and it currently has 166,000 miles. No troubles at all, just oil changes. Got super lucky, it was owned by a racing mechanic who just used it to tow his race trailers to the track on occasion. Very well taken care of.
It came chipped with a Hypertech II controller which makes an immense difference. You don't feel it just driving around, but you feel it big time when towing. With the huge engine and higher boost, you feel like superman. you can tow anything and go up any hill. It also came with air adjustable rear shocks which makes a huge difference when towing. It is extremely stable on-road, but it is also very stiff, so does not do well off-road. (it is a 2WD model anyhow) one day I'd like to find a balance between towing stability and ride quality. I think the shocks in general are also just worn out. Very expensive replacement so I won't be touching them for now.
One thing I'd like to add is a set of pillar gauges for boost pressure, temp, etc. I really have no idea what's going on in there and it would be good to keep an eye on it when pulling hard up steep passes. A cheaper option would be one of those OBDC adapters for your smartphone and an app to go with it, but then if you're using the phone for navigation you can't do both at the same time. I suppose there could be a second throwaway phone used for the OBDC when towing.
I haven't had any problems with the transmission at all. I am not sure if the 250 and the Excursion share the same transmission?
I haven't done anything to it but change the oil and tires since I bought it at 93k, so it is probably due for some preventative maintenance. Changing the transmission fluid sounds like a good idea, per a previous post.