I borrowed a Versa64Card from my friend @giomba.
To help diagnose the fault, he pre-programmed a flash with 4 different diagnostic ROMs which can be switched by holding the top address lines either high or low.
Of these, Dead Test has the best chance of running on broken boards: it sets the #C64 to "Ultimax mode" and doesn't rely on the KERNAL ROM. In fact, Dead Test can run with most chips pulled out except for the PLA, VIC-II and, of course, the CPU.