Try putting a dab of grease on it and then torch it until the grease wicks into the threads. The heat cycle will expand the alloy before the steel. The grease melts well before paint damage. Then try your various methods.

Success - I bought a set of five HSS 3mm bits and used them in succession until I broke through which happened in no time at all. This allowed me to use my screw extractor bit to complete.

An unexpected bonus is that the threads appear undamaged as the new mudguards are now firmly in place.

Thanks to you all for your kind attention and knowledge.

How's that different than any other thread?....

I might have missed all the steps you've used - but have you tried clamping the remaining part of the head with a vice-grip type of tool and turning it off? It appears from the photos that this might be possible, but maybe I'm not seeing the photo accurately.

I have used left hand drill bits to drill out broken bolts.