I'm not sure what adding calcium to meat will do to it, but I'll comment on the rigor mortis side specifically.

Was looking at how rigor mortis is caused and found out it's from the body leaking calcium into the muscles.

It's true that calcium is involved, but it's not because it leaks into the muscles. I found this open textbook that covers the details:

https://open.oregonstate.education/anatomy2e/chapter/muscle-fiber-excitation/

I think what you're referring to is this bit:

• Cells use up something called ATP to run a lot of the machinery
• When muscle cells get specific signals, they use ATP to move sodium and calcium ions around in order to do the contraction/relaxation
  • In particular, calcium is released from the SR (a container that sits inside the cell) into the cytoplasm (the area outside the cell) to trigger contraction.
  • Later, to relax again, calcium is actively pumped back into the SR using ATP
• When the cells run out of ATP (because the person is no longer breathing after death, and so the body can't make more ATP), the muscle cells get stuck in the contracted state

It's a bit more complicated at the tissue level, but that's more important for the macroscopic changes we see during rigor mortis. Individual cells contracting isn't enough for us to contract our muscles at that scale. We also need the fibers to pull past each other.

In particular, the "myosin heads" grab onto "actin filaments," and pull themselves along, and they use ATP to detach each time.

Which brings us to this bit from the link:

Note that each thick filament of roughly 300 myosin molecules has multiple myosin heads. These myosin heads cycle asynchronously to maintain constant tension in the activated myofiber. During a muscle contraction, many cross-bridges form and break continuously. Multiply this by all of the sarcomeres in one myofibril, all the myofibrils in one muscle fiber, and all of the muscle fibers in one skeletal muscle, and you can understand why so much energy (ATP) is needed to keep skeletal muscles working. In fact, it is the loss of ATP that results in the rigor mortis observed soon after someone dies. With no further ATP production possible, there is no ATP available for myosin heads to detach from the actin-binding sites, so the cross-bridges stay in place, causing the rigidity in the skeletal muscles.

I'm not sure if it's possible to trigger a contraction manually using calcium alone, and you likely won't be able to do it with regular meat because the proteins break down within a few days after death (which is why rigor mortis goes away after a while).

You could look into how they trigger contractions in muscle fibers in the lab