I recently did a project in a 70 foot planetarium (more on that soon) and wrote some code to handle fulldome style fisheye rendering. I just finished pulling it out and wrapping it into a block. The README goes into detail about how to use it, so I won't repeat it here, but check it out on github. The short version is that it uses four cameras, and four render passes, to render to a circular fisheye image which most professional dome systems accept for input.
At the installation, I had it rendering 4k by 4k at 60fps on a PC with a Quadro m6000. It was super fun and rewarding to work that large and immersively, so if you ever get the chance, jump at it! Hopefully this code helps.