>>It's easy to see why it's a particularly tricky problem to overcome, as the solution in my experience depends on getting both the iron and the cap iron back into working shape, and then ensuring that the sharpening method employed keeps the iron in decent condition.<<
Yes, on the experience. Once it's ironed out, it becomes simple and trivial, but most of what we can do reliably in life (that's worth doing) is that way. Because of my fanaticism, i always flatten an iron properly and geometrical "perfectize" the leading edge of the cap. So my experience with these two types is after the caps have been cleaned up and match the iron without much pressure.
I just found that the SS types didn't quite fare as well, and I was stuck more often taking the plane apart to get stuff out. Perhaps that's once every couple of sharpening cycles, but I don't like it at all, unless there is an excuse (cocobolo is one of those things where the early wood is so hard that it creates stiff little wafers that will still creep through once in a while. When it occurs on cherry, beech, oak or maple or something like hat, then I'm out and on to something else).
What I experienced is probably much different than what someone who rarely uses the cap iron will experience. In that case, the stayset is nearly ideal, because there's nothing to reset, the cap probably isn't that close to the edge to begin with, and you don't need to:
* find a screwdriver to take the iron and cap apart
* lament that you have the odd plane here or there were the lever cap can't fit in the cap iron screw slot to alleviate the need for the prior bullet point. My favorite jointer (a superb sorby no 7 - suffers from that problem , and eventually I will file the cap screw slot wider to fix it).
There's something about the bailey cap iron design that just allows it to stay shut on forceful chips just a little bit better. And that point is only worth noting if some adherent like me is choosing between the stayset and the regular stanley/record type.
Too for the americans, I ordered my staysets from england. Shipping globally is expensive (and risky now if you choose to use the GSP on ebay - it's to be avoided due to their proclivity for confiscation of things that shouldn't be confiscated), but even after accounting for the cost of global shipping and then the subsequent ebay fees, I lost nothing in trying those three planes other than a little time.
The same can be said for decent record 4 1/2s, which must be in abundance over there. I got two for effectively $30 plus another $30 of shipping charges. They sell easily over here for $85. You get a "free look" on those kinds of things.