Of course it is too soon for me to be able to provide reliable data on the efficacy of the high(er) power desulphator which is now limping-on with a hot(tish) transistor.
Last night (actually 08:30 this morning) I had rigged it to a 19 A/h battery and when I was reasonably sure it was OK, I left it to be pulsed. (So I could get some sleep).
The next time I tested it it was done. I finally did a SG test after it had been pulsing for about twelve hours.

So I was unable to watch the progress of the desulphating because the sulphates appeared to be gone.
That battery must have been a wierd one. From the start it was overfilled. All of the cells wwere over maximum and three of them were approaching the top of the battery case.
Usually when a battery is overfilled like that it will have a low SG reading. But All the cells were at least in the green (over 1250) and the ones which were only overfilled were well into the green. Strange.
I would guess the pulse rate was in the region of 2 pp/s at a current of over 20 A. I've got around 16,000 mFd caps charged to about 42 V being pulsed in 100millisecond pulses.
Unfortunately I have had to rebuild some parts due to component failure (murder), but thanks to having pretty-coloured wires with croc clips on each end I have it running.
I just wanted to provide my preliminary result from my experiment with pulsing at a high amperage in a fat pulse (a thunk is probably not the scientific term for it).
The transformer I'm using is rated at around 50 Watts, and it is certainly delivering well over that. It remains viable due to a (computer) fan blowing on it. The transistor I'm using is mounted on a 'U' shaped heatsink with the flat side up, and the fan is mounted underneath it with a hole the diameter of the blades cut into the wooden base. The air hits the top of the heatsink - under the transistor and is then blown out of each side. On one side is the main transformer which charges the caps, and the other side is a smaller transformer which I am using to power the gate/base driver.
I'm in a sort-of hurry to find some semiconductors I can use without worrying. I'm using a transistor due to it being the only thing I can find which will survive the amperage, and I'd much rather use a MOSFET.
The base of the transistor is drawing up to 4 A at max, and this will take its toll on the (somewhat large and noisy) relay I have settled on. - A small relay rated at 3 A was toast in half an hour. - I mean the contacts welded themselves shut. I am wondering whether they'll last much longer either in a relative vacuum or running in a mineral oil bath? I Might try this potentially awkward and messy experiment at some time.
* These days I am fairly selective with choosing the batteries I deem suitable fo an attempt at desulphating. I'll reject the ones with seriously corroded plates. I think those with disintegrated plates may work well. But I doubt they'd last long, and I would imagine the capacity of a battery with crumbling plates would be appreciably less than one in which the plates appeared sound.
Slow & high-A pulsing???? Hmmm!

So far so good.
What has been won by the brave at great cost can be lost cheaply by fools and once gone can rarely be regained and only then at great cost.