Thanks for the suggestion, Julie. I'm no expert, but I don't really know if dry ice could freeze through 2 inches of solid concrete. But it might make the ceramic tile on top brittle (which would be a help). But it's a long way down before I'd see any plywood.
And that's the major problem Greg. 2 inches of concrete. It's already too heavy and too high. If I add anything else on top of it, I'll actually be creating a small step - from the parquet up to the ceramic.
In the picture, it doesn't look like 2 inches of concrete because of the slope of the threshold, but when you take off a vent cover (in the hallway) you can see the full brunt of it. And I'm guessing there's mesh under all that too.
But I like that you and Royce believe I can have it removed for $1200 or less. I'm willing to pay that much. It's worth it for a totally fresh start and to be able to put in some really great tile. Thanks so much - you've definitely given me a great solution (and I won't even have to do any of that demolition myself