Dave Curran wrote a post on his blog showing how he upgrades the ZX81 internal 16K RAM with a reversible version:
One of the common issues with the ZX81 is the good old RAM pack wobble. Depending on the state of your edge connectors on your ZX81 and RAM pack, it sometimes does not take much to interrupt one or more connections and crash the ZX81.
To get around this, I have done many ZX81 internal RAM upgrades, following the procedure I described in an old blog post – ZX81 Internal 16K RAM.
I had a request to do one of these, but to do it in a reversible manner, without cutting tracks.
See the full post on his blog- Tynemouth Software.