I would load up the SR5 and go down to AAA, they can verify (dash, door plate, engine plate or the firewall) the car against the pink slip.
If they happen to ask about the engine not being installed, tell them you are in the process of getting it restored that is why engine is not installed and the reason you want to put it on non-op is because it will take you lot longer then you had initially thought.
done it many times with zero problems
For added insurance you can take the original 2tc with you (not installed) just to show them that you do have the original engine. (I doubt if they will be able to verify what car that engine belongs to)