I will try and report back ASAP.
Thanks, AaronP, disabling MSI helped and now I'm able to load nvidia.ko module at anytime.
However my GPU now shares an interrupt with a USB controller:
grep -i nvidia /proc/interrupts
16: 25 80 16 116 IO-APIC-fasteoi ehci_hcd:usb1, nvidia
which I don't much like but I can live with.
Alan Cox said exactly this: "It's a non free driver only they have the source to all the parts so only they can debug it."
And as expected the bug
was closed as INVALID.