I ordered a new starter last week and it arrived yesterday. Got it installed tonight and truck fired right up. Thanks for your help everyone. I went with this one:
M8T50072 Mitsubishi Gear Reduction Starter for Ford Diesel FORD TRUCKS 7.3L
I called the place before I ordered and talked to one of the guys there. He has the same truck as me ('01 F250 7.3) and runs this same starter on his own truck. It sure turns the motor over fast, and has a very different starting sound than the old one did.
Make sure you have the right bolts in there, a lot of these trucks get 3/8 bolts thrown in by backyard mechanics; and eventually with the higher torque they loosen and your starter will sound like you held the key too long, or it won't engage at all.
They're supposed to be 10mm theads, 1.50 thread pitch, 40mm thread length. I had the wrong ones in and they kept loosening, and just about stripped the bolt holes. I caught it in time, put in the right bolts, and lock-tited the hell out of them.
Check your starter bolts! - Ford Truck Enthusiasts Forums