I had a similar experience when I was a student. I was on solo status, but not packing my own chute yet. Had a lineover and started spinning since the right half didn't inflate.
Luckily I was on a student rig so I doubt my spin was as violent as yours. Also I was on a single handle system so I didn't worry about stabilizing myself before pulling the reserve. I pulled my reserve handle probably by about 3.5k and was able to keep both the reserve handle and ripcord.
I landed and got on the sunset load 15 minutes later. Later I had the rigger tell me that its almost impossible to pack a lineover so I probably didn't have one. I wonder if he still thought that after they recovered my chute. Good job getting back in the saddle!