I maintain a primary disk image with all the games installed. During a party, all the machines boot from that same image, except each with a private copy-on-write overlay. Any changes made on a machine are written only to the overlay. At the end of the party I delete the overlays. The primary image remains in exactly the state it was in before the party.

So before each party I just have to install updates on one computer, like a normal person would. No need for a special cache. (Or arguably, the primary image is the "cache".)

Full details and code in this github repo: https://github.com/kentonv/lanparty/