All these people with access to / able to build plasma-cutters (sounds like a recipe for disaster) and spark eroders…
I persevered with the potassium aluminium sulphate, successfully.
It went something like this:
Friday eveing: put the part in the solution overnight.
Saturday morning: rinse it to remove residue (the drill had jammed in a blind hole), add a bit more sulphate to the solution. Leave it all day.
Saturday evening: make a bain mairie by standing the glass jar of solution with the bronze part, in a medium-size saucepan of water. Raise the temperature very gradually from cold so as not to crack the jar. Set the water simmering on the gas ring’s mimumum, at slightly below boiling.
A fine plume of what I took to be microscopic bubbles steadily rose from the hole, but not being a chemist I don’t know what gas they would be. At a guess, possibly hydrogen.
I turned the gas off after about three hours and left it all as-was overnight.
Sunday (this) morning: The broken steel was still in residence though diminished in length. I re-lit the gas, set the water just simmering again. When I next looked, about three hours later (apart from occasionally verifying there was still water in the saucepan), the steel had all gone but the bronze was untouched, not even discoloured.
So yes, the method does work. It doesn’t need specialist equipment or trying to find companies willing to carry out the work for you – at a fee. Just patience.
I accelerated it by keeping the solution hot: once it was all cool I put the lid on the labelled jar of K-Al-SO and put it away for future reference.
Carried on machining the part, only to have one problem after another with trying to hold the wretched thing, a three-way pipe connector, securely, square and centred on the holes so I could machine the exterior around them. It is very small, too small for my Myford’s hefty lathe chucks, and an unusual shape. It ended in failure and I have spent this evening starting another to the same form but using a different machining approach. And brass not phosphor-bronze.