I've got a few alternative options for handling tear out on flat boards, but not too many for curved work. A card scraper or a high pitched HNT Gordon spoke shave are my usual solutions, but the shavings are so fine with these tools that it's a lot of work to remove tear out on curved components. Often I just go straight to a bobbin sander, but that carries a big risk that the fairness of the curve gets compromised, something that's difficult to spot until the finish gets applied.
So if the finely set cap iron works on a compass plane that would be a big and useful step forward. Inspired by DW's video I just tried a "proof of concept" on a Bailey plane before giving it a go with a compass plane.
Here's an I Sorby Bailey style plane with the original thin iron (maybe a bit thicker than the usual Stanley/Record irons but not by much). It's been well used but not by me, and it's never been sorted out. The iron needed grinding, honing, and the back flattening. The cap iron was a quite "gappy", but that was easily sorted out. No more than 15 or 20 minutes work got it to this stage,
I used an off-cut of highly figured Curly Cherry from a Shaker chimney cabinet that I'm currently making. It's been a problem timber, needing back bevel knives on the planer/thicknesser and multiple passes through the drum sander to keep tear out under control.
I set the cap iron a few tenths of a mill back from the edge and started with some very thick shavings, much thicker than I'd normally use, but absolutely no sign of any tear out,
Then moved on to finer shavings, tried planing the board both ways, still zero tear out,
I was fretting about blunting the edge by running the cap iron over the honed edge when setting it (I think David Charlesworth mentioned having a similar concern - I've got in the habit of treating a honed edge with extreme reverence, maybe it's not really warranted?). I actually did run the cap iron over the edge a couple of times, but in practise it didn't seem to cause any problems and the iron still cut well. I'm sure with a bit more practise at setting the cap iron extremely close this wouldn't happen so much, and in any event I'd be less anxious about it in the future.
What can I say, so far at least it works!
I'll put a bit more work into the plane and try again tomorrow on some other problem timbers. And if it still delivers good results then I'll move on to doing the same thing on curved components with a compass plane.