Several observations, Bob-
I wouldn't call it welding unless you find intermetallics in the wire, glass, or both, and a heat-affected zone in the wire (indicates localized melting), and there's no test results or at least something qualitative like photomicrographs to indicate that. Intermetallics, because significant alloying with Si, Na, K or other metals common in glass would be normally very unlikely without the wire melting in such a brief time- but if charge cluster behavior is the governing parameter here, then very exotic alloys COULD be present in appreciable amounts, and that would be even more significant.
I've never seen anyone try an A-B cutting or welding test between HF-produced hydroxy/Brown's gas against a conventional oxy-hydrogen torch- the charge-cluster explanation is still not very rigorous, (I have nothing at all against this hypothesis)
- but your test for that needs to rule out the effects cutting the billet has on oxidation rates- necessarily exactly in half, as well as ruling out magnetic gradients there from the cutting and surface removal- maybe just face both samples? Maybe laser cutting? This gets very slippery trying to collate the data to intermediate state to initial input.
Some of us (I hope) are familiar with some glassworkers' techniques- you can take a hot enough blade and "cut" holes in glass without cracking, or the classic way to cut tubing with a polished edge, a garotte of hot resistance wire drawn tight.
Face cutting both would be easiest and a start point.
Some studies of 'welded' surfaces would be useful, however, just like with the Hutchinson fused dissimilar materials and the filing cabinet from 911 (apparently managed to 'melt' but not burn paper) I would expect them to only have inter-metallics or alloys where pure metals interacted, and even then rarely.
Just look at how that thing 'melted', kind of like scrunched up, but in a plastic amorphous way. I used to run a burger stall on a Sunday for years, with a charcoal barbecue in half of an oil drum - I never saw anything like this.