Slamming a T-350 into park at speed is probably only going to break the parking pall.....
Sounds like the trans is gone but there is one thing you can try. If anyone you know has T-350 parts hanging around, see if you can get the valve body from them. Buy a BM shift kit (for the gasket and instructions) and change it. The fact that you lost it all at once would sugest to me that the clutch pack is OK, and that its an obstructed orfice. The valve body controls flow to the 3rd gear apply hub (what pushes the clutch pack together to engage 3rd)
Thats something you can do with the trans still in the vehicle.