You could use a RT to do what you want. The TM1 is RT ready, but a 12'' Haas RT is expensive. The other downside of doing what you describe is having to override the door safety and have an operator working near moving tooling....... Not good.
Since your parts are flat-ish, why not make interchangeable pallets to mount the parts on. Have two pallets, load/unload one while the other is running. That way the machine down time is minimal. I would set them up so they just clamp in place, located by dowel pins.
I would also load up as many parts as will fit on the table.
We built a tooling plate that stays permanently attached to the table, then make interchangeable pallets that attach to that which gives us a very accurate quick change system.