The only thing electronically controlled on the 32RH is the torque converter lock up. Everything else is purely hydraulic. It sounds like the centrifugal governor is sticking and not allowing enough line pressure for the trans to shift. A very seasoned transmission guy told me that when that would happen on the torqueflites, he would take it for a drive and stay at 40 mph. Once he was there, he would throw it into park. What happens is the parking pawl is trying to engage onto the teeth but can't at that speed, and the ratcheting that it creates vibrates the governor and causes it to unstick. If you feel like changing the governor, it's not too hard to do. It's located on the tail shaft on the back of the trans.
Hoist and support vehicle on safety stands.
Mark propeller shaft and axle yoke for assembly reference. Then disconnect and remove shaft.
Disconnect parking brake cable at equalizer and disconnect exhaust components as necessary.
Support transmission on a suitable lifting device.
Remove skid plate and rear transmission mount.
Remove transfer case and extension housing.
Loosen but do not remove bolts that hold governor body to park gear.
Rotate transmission output shaft until governor weight assembly is accessible.
Remove E-clip at end of governor valve shaft (Governor Valve).
1 - E-CLIP
2 - PARK GEAR
3 - CURVER BOSS
4 - GOVERNOR VALVE
5 - GOVERNOR
Remove governor valve and shaft from governor body (Governor Valve).
Remove snap rings and spacer that retain governor body and park gear assembly on output shaft (Snap-Rings And Spacer).
Remove bolts holding governor body to park gear (Governor Body).
Separate governor from park gear.
Pull park gear from rear support