OK, problem resolved after taking the old center diff apart. The rear drive transfer shaft, shown with the two spline sections, doesn't actually engage with the front drive beveled gear in the differential. The bevel gear, and the front drive shaft do rotate with respect to the spider gears and the rear drive beveled gear (open differential). Just not in my specimen. I needed to use vice grips to rotate the front / rear drive shafts because my viscous coupling device is nearly frozen. I heated it up a little to 120F, and it locks up completely. Put a used center diff back in the tranny, and it seems to work fine.
For prosperity, here's how to check if your center diff / LSD is failing. Jack up the vehicle from the side, so that the front and rear wheels on that side are off the ground. Parking brake off, tranny in neutral. Rotate the front wheel forwards, and the rear wheel should also rotate forward. Now put it in gear and repeat. This time the front wheel forward should result in the rear wheel rotating backwards, reverse.
In neutral, the center diff housing rotates freely, allowing both drive shafts to move forward together. In gear, the center diff housing is locked by the tranny and engine resistance, forcing the front and rear drive shafts to rotate in opposite directions. When I do this, it's very stiff, but the wheels rotate in opposite directions. I'm assuming under normal conditions the two drive shafts only need to move a little, and slowly, with respect to each other