How to remove broken light protector/cover from inside oven

I bought a 6 year old house, and the Previous Owners did basically zero maintenance.

The oven is a Bosch underbench electric unit, and it looks like the glass cap/protector for the interior light has broken off at some point, so they kept using the oven with the lamp exposed. The lamp does turn on when in use. I expect this has been left like this for at least 2 years, maybe up to 6 based on the condition of the rest of the oven.

This leads to a threadded glass ring welded into the fitting by dried/hardened food/oils, and looks like this:

I've got the replacement cover already, and its essentially a very short glass jar with one thread around the top so I know this ring should unscrew conventionally.

I've tried blasting it with conventional oven cleaner to dissolve the shite, but its not getting into the threads.

I've tried some other solvents like "Contact 60" an electrical contact cleaner, and some other household liquid cleaners hoping they'd wick up the threads, but that's made no difference.

There's around 4mm of "neck" exposed so I can grip it with one hand and rotate, but the whole light fitting is loose, and I don't want to overstress whatever mountpoints are there. The glass is sharp too, so can't put too much pressure on it, even with a teatowel to hold it.

• Do I have to open the oven and remove the whole light assembly, then work it on the bench?
• Should I try to break the remaining glass with a hammer, or alternating heat and cold like cutting the neck off a beer bottle? Feels risky.
• Or do I give up and get a service wallah out to do it?

Edit : Here's the new fitting, to show what the old one will be like: