I think you could do that today? Incubating a cell culture is definitely possible. You can either purchase used lab equipment, or even build your own incubation chamber.

I don't think OP's chicken heart experiment requires genetic tinkering, but even if it did, my understanding is that CRISPR is surprisingly accessible to hobbyists. For example, https://www.the-odin.com/diy-crispr-kit/.