However, after some time spent Googling the problem (again) and generally doing a lot of whingeing about it, I saw someone mention way down one of the pages I was poring over for help, that they used flux on their wire. I can't remember where I saw it, nor can I find it again (naturally) or I'd put the link here. But 'Aha' I thought - flux. So I looked up flux on some of my supplier sites, only to realise there are lots of different types, and I couldn't find one that suggested it could be used on brass. I asked on my Facebook page, and a very kind follower advised that although she used it for silver, her preferred flux was borax.
I figured it was worth a try - at the very least, if it didn't work, I could try it on my sterling wire. So, one borax cone and a dish later, I sat down this morning to experiment. Painting the wire with the flux paste is fiddly and time-consuming, but when I put my brass wire in the flame, expecting a mini fire again, it was not so! A teeny tiny ball formed on the end of the wire and did its fascinating spinning around and crawling up the wire thing. It's going to take some practise to get the balls a bit more central, and it's not as easy as bronze - but yay! Result! :)