If you put the gear selector into P and the car rolls, then your trouble is somewhere in front of the t-case, I think. Maybe the t-case itself. If the car is in P, then there are pawls that are pushed into the output shaft to keep the car from moving. Your issue is more global than an individual driveshaft. Something common among the driveshafts has broken, allowing the car to roll when in P. The commonality is the t-case and the transmission.

The stripped splines would keep the car from going, but they should not keep it from parking.

The t-case is a differential, of sorts. It distributes power fore and aft based on slippage, if the front driveshaft is slipping then all power will be delivered there and the car will not go. But the rear is still connected and the car should stay where you put it when you select P.

If the chain or related parts failed within the t-case, then the wheels would not be connected to the transmission at all, and P would not do it's job. Of course, D would not work either.

Me thinks you have t-case troubles, not just front driveshaft issues.