If it were me, I'd use a tester to write specific patterns into the bits and then check the output to see which bits (and thus which RAMS) were bad. But you'd need either my Arduino tester, a Fluke with a Z80 pod and 2650 adaptor or to write your own test ROM to do that

It also looks like you may have some other issues since you're seeing whole characters all over the place that suggest a program ROM or RAM issue.
If you decide to invest in an Arduino tester, there is a guy on UKVAC who's done a run of 10 PCB's and thus has a lot of spares available. I haven't added support for Dodgem/Invaders to it yet, but I'll try and make a start on that over the Xmas break.
Paul.