I'd actually be encouraged to see donated organs cryopreserved, and used for transplant long after their unpreserved expiry.

When we are using cryopreserved organs, then preserving the brain becomes more obviously pragmatic.

I am guessing that cryopreserved human kidneys do not have uniform cooling, spoiling interior tissue. A rabbit kidney is much smaller, and wouldn't suffer as much from this problem.

This is currently happening with ovarian tissue: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6558345/

Hmm... maybe it would work better if you actually circulated chilling liquid through it, rather than just sticking it in a freezer.

The interior veins and arteries of a kidney look like it would be a reasonably good heat exchanger.