Thanks for suggestions. Encouraged by Clive's response (it should be possible to weld down to 1mm with MMA) I had another go today. I realised that when I strike an arc I instinctively withdraw the electrode a bit then move it back in to correct the arc length before starting to lay the weld. This takes only a fraction of a second and isn't a problem with thicker stock, but it seems to be too long for such thin stuff. I worked on improving this aspect of my technique and had some success, though I had to cut the sticks down to about 4 inches to get the necessary control .
I have now made some ugly but sound welds by laying sort of extended tacks, cleaning up, then joining them. This seems to work – I'm trying to make T joints and it's harder to do the fillets than the sides, but for this project (it's a lightweight frame for a prop horse) I probably don't even need an all-round weld.
I took on board Noel's suggestion that it might be better to up the amps rather than reduce them and that seems to have helped too. I am using 1.6mm 6013 rods and was running at 15A. The recommended amperage on the box is 20-40A, but some guy on youtube told me it was OK to 'run cold' for thin stuff. It seems to work better at around 20-25A. I could lay test beads OK at 15A, but not so good for actual joints. I'm not sure why yet.
The upshot is that I now think I can do this without investing in new equipment , which is good in one way but bad in another – everyone likes a new toy! But as I have now sort of mentally budgeted for this sort of money for welding I think I might have a go with TIG – my MMA machine (Parweld 163) has a lift TIG setting and I can buy a torch and gas bottle/regulator for about £200.
Thanks for the suggestion of the Albee gas Clive – I was thinking Hobbyweld, but the small Albee cylinders are actually cheaper for the gas (because they charge them to 200 bar rather than 137 bar from Hobbyweld)
Mark and David – many thanks for your generous offers of help with this. I'm in Derbyshire, near Matlock, so a bit too far away. Much appreciated though.
Robin