Some years ago I posted observations of thin iron chatter, which can be seen as dial guage flutter during a planing stroke. The blade lifts from the frog. The effect is mimiced by putting a flexible 12" rule over the edge of the bench at the 1" mark, attempting to hold the 11" down with 2 fingers whilst loading the tip. The often quoted need for all over bedding to stop chatter is false, provided the heel of the blade has a firm base. The 2 piece cap iron does indeed improve matters, but it is difficult to arrange a close setting because there is so much backlash in the 2 piece coupling, and the shape does not suit blade cambering very well. The MF levercap looks like a positive benefit, probably later lost as MF engineers (accountants?) forgot what it was for.
The best and simplest solution I have found is a simple , completely flat cap iron, "sharpened" at the business end, and with a small hook rolled scraper style to prevent shavings being trapped. This arrangement can easily cope with a cambered blade, as the cap iron may be cambered the same way. That way you can have a close setting right across the cambered blade. The lever cap can exert enough pressure to flex the cap iron firmly against the blade so no chatter. With this arrangement the cutting geometry is getting close to a scraper plane, with the addtional benefit of a close mouth. Handy when you need it. Simples!
By the by, Hayward (ed. Woodworker mag.) suggested that low gringing angles for the bezel can cause chatter due to flexing in the ground section of the blade, so for difficult stuff a single grind/sharpening angle of 30 or 35 deg should prevent this. It would appear that a thick blade could also suffer in this fashion; something known to the Japanese carpenter, perhaps.