BSOD on startup once any program is opened, error BCCode 116

How long did you run it for? 0x116 errors mainly indicate faulty GPUs, but they can be caused by drivers.

I ran it for about 30 minutes on both machines, until the temps leveled out.

Honestly I'm running out of ideas so try and take a look at this

STOP 0x116: VIDEO_TDR_ERROR troubleshooting

Alright, it seems I can't determine the exact cause either.. Will look into replacing the GPU, is this possible on a laptop with the NVIDIA Quadro FX? I have only replaced them on desktops before.

I've been asked a similar question before and I can't answer because it depends on the motherboard, most likely no.
However you can ask here and they may give you an answer.
I don't have much time to go looking for which GPUs are compatible.

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