Either Ditra or cement board, embedded in thinset is fine. I prefer the Ditra. Having said that, you need to scrape up as much of the mastic as possible. Dampen the mastic and try a 4" scraper. You may not get it ALL up, but flatter is better.

StoneTech,

Thanks for the answer. If I get the mastic flatter, is
there no concern about the thinset under the Ditra adhering
okay to the subfloor? Is there a special type of thinset
that adheres better to mastic, or a primer or some such?

It is about 380 square feet, so in any case, quite a bit
of scraping. A bit of it may also need some leveling
compound.

Get as much of it up as possible. You can trowel some "loose" thinset over it with the flat side of the trowel to flatten it out a bit, if needed.

You need to use a modified thinset for all of this. Home Depot sells "Versabond," which will serve you well. White-gray, makes little difference. I wouldn't worry with a primer.

My tile is 3/8" thick, 13"x20"

How thick will the total be, thinset-Ditra-thinset-tile?

5/8" to 3/4" at most...

Closer examination of the old attach material makes me think that maybe it isn't mastic. It is gray, looks a bit plastic, like JB weld epoxy. Soaking in water for 20 minutes doesn't affect it. My belt sander, with a super coarse belt, pretty quickly turns it to powder, with no tendency to melt, which I've been told that mastic would.

Any idea what someone would have used in the 60s to directly attach tile to plywood subfloor, that matches this description?

I had the mastic checked for asbestos. The report came back 2% asbestos content.

Any further suggestions on removing this mastic? It sands quite readily, but that seems a bad thing, maybe even if wet.

What is the subfloor under the mastic? How many layers of plywood? Is it up to the task of dealing with your very large tiles? What tile material?

You need to confirm that your subfloor is adequate for your new tile. You may find that you need another layer of plywood on top of what is already there, so don't kill yourself scraping up toxic mastic just yet :)

Yep, Tim, that's what I'm thinking. The subfloor is 5/8" t&g plywood. The previous ceramic tiles survived 48 years without significant issues, but they were small, maybe 5.5 - 6 inches maximum (the 4" in my original post was wrong). I'm going with stronger tile (Daltile Ayers Rock), but at least 13", so a stiffer subfloor would certainly be better.

Not removing that existing mastic would add a bit of height under the plywood. Looks like the stackup (mastic, 3/8" plywood, Ditra, 3/8" tile, maybe some leveling) would hit 1", which means I'll have to add ~1/4" plywood under the rest of the flooring in the house (solid hardwood for some, cork for the rest so that needed more height anyway).