You do not mention if the "rebuilds" included the installation of grounded 3-wire AC line cords. Also, what happens if you unplug the 6AN8? One possibility is that both amps may have been connected to something with a "hot" chassis and the grounded line cords did thier job and burned up some ground connection/PC board lands on the MK-IIIs, thus preventing you from being shocked.
Otherwise, it sounds like your problem is in the front end somewhere. This whole thing smells like a bad ground somewhere, but it's interesting that it happens with both units at the same time. That would suggest either two problems exactly the same with both units, or perhaps a bad ground in your house wiring as previously noted.
But is the can cap soldering of the chassis actually good? It's amazing how many techs to NOT have large soldering irons that can not put out enough actual HEAT/BTUs to do the job right.
If the can soldering is good, then the next thing I would do, as a test, is to ground one of the amps to a cold water pipe by literally connecting a piece of wire from your bathroom or kitchen sink's cold water pipe to one of the amp chassis. Connect to the cold water pipe FIRST. Be careful; you might even want to wear pair of gloves when you do this; I don't want to get sued for trying to help you
If the hum goes away, then it's time to stop right there and call a licensed Master Electrician and have your house wiring checked, starting with the ground rod.
If proper grounding is not the issue, I would be looking over ALL the other connections on the amp for starters. Then I'd be looking at the "new" filter cap cans. I say this because IF it's component failure in both amps at the same time, THOSE would be my third, though less likely, suspect. Even IF the plate supply filter for the preamp stage was bad, I don't think shorting the input would eliminate the hum as you stated. I mention this because I've had a LOT of trouble with the cans supplied by CE Distro, so much so that I was getting them from a different source, Dynakit Parts. However, Kevin at DKP recently told me he too was obtaining some of his can caps from CE. So I'd call him and confirm his source before ordering any if needed. Finding good reliable can caps is SO difficult now that my last few McIntosh customers elected to have me disconnect the old cans, leaving them in place, and replace them with good old (new) Sprague axials under the chassis.
All that being said, you should also, of course, measure the resistance values of every resistor in there. But again, it is very unlikely that the same two resistors would drift up in value on two different units at the same time. But confirming resistor values is always a good thing to do, especially with old carbon composition resistors. I believe there's less than 20 or so of them in there.
Though I rarely post here, this has really sparked my curiosity. So please DO let me know how you make out.
Good luck and best wishes.