How high can a ‘sub floor’ be raised withh plywood sheets

One comment on the advice you read is that I don't see a thing in there about deflection - evidently Mike Holmes is sure that if he merely has 1-1/4" of subfloor, all is good. Real tile specs tend to involve a concept called deflection, and that's the distance part of the floor system moves when loaded, relative to the span you measure over. L/360 is a typical spec - L/180 is twice as bad. (It's usually a lowercase L, but on the computer I'm using a capital to be clear that it's an L.) I happen to have a 3/4" subfloor that's L/587, so it really doesn't need another half-inch on that basis.

Consider what a tile manufacturer has to say... (I'm not going to cut and paste their extensive text here, or rewrite it all) but for one thing they specifically mention setting the backer board in a mortar bed, not "gluing" it down. I'd also venture to sneak in that if you really want "the best" (and will you pay for it these days) look at the "old fashoned mortar bed" (TCNA (Method F145-02)) mentioned at the end of their article. That, of course, means you need to establish an adequately rigid base 3/4" or 1-1/4" + tile thickness below the surrounding floor level, which is why it's not popular these days. But it was a VERY good method, as a lot of old houses demonstrate.

Kinsman Tile

I don't have any experience to say for sure one way or the other (except that I've not had any notable vibration problems with my front load HE washer on the first floor, which is just sheet vinyl on 3/4" plywood, near the end of the joists). But what I'd think you want is basically the same thing that that you want when you're soundproofing a floor; you don't want vibrations at the top to transmit elsewhere.

When soundproofing, what you really want is a sandwich of plywood, underlayment, plywood. So roughly what you're suggesting. Cork can work well, though rubber underlayments generally perform much better at the same thickness. You lose a lot of the benefit if you screw the top layer to the lower layer, though - you want the layers glued together, without anything hard bridging across the soft layer.