Crashing A1200 + Apollo 1230 Mk 2

[stachu100]

It can be the problem with:
1) Turbo card (CPU) is too hot - most probably the case. Please install fan on 030 CPU.
2) Not enough power from PSU - try different PSU

[stachu100]

I've also noticed some graphics corruption; I think I'm using a productivity mode (640x400?)
 
Have you ever checked temperature of IC's on A1200 board?
The artefacts mentioned by you occurs when temperature of the IC's is too high.
High resolution graphics modes are "very stressing" for AGA chipset.
 
So please switch to standard PAL resolution and I think your problems will gone.

[stachu100]

Is DBLPAL enough in itself to heat the chipset this much?

Yes