An ignition stator coil outputs up to 500V peak when supplying power to CDI, so it is not at all easy to test.
A coil resistance measurement does not tell you much about the magnets, coil insulation etc.
A "Direct Voltage Adapter" seems to be just a 1/2 wave rectifier diode+cap+resistor which works as a peak detector.
I think your multimeter is OK but the DVA may have blown up. A 600V reading means the cap inside must have popped. Take it apart, post pics

edit: I did check the Fluke 88 Automotive Meter schematic and the voltage channel is well protected. Above 1,000V for a long time it will start to burn a resistor inside.
Because CDI is very noisy and makes a lot of interference, it was likely too much spikes (for almost any multimeter) when connected to the stator coil hot side, so it crashed.