You would for sure have to screw down any plywood subfloor. However it's not a great idea having concrete and plywood touching anyway, even in a 4th floor condo. And using tapcons is annoying. Dricore is the perfect solution except that it would add too much height...7/8's. I've not seen it done this way, but you could probably use 4x8x1/2 inch tongue and groove osb to create a floating subfloor. People use this on top of rigid foam in basements, so it should be fine although it is still wood touching concrete. -- It's overkill but the best solution is probably back to Ditra. You can get the exact height you want and you would be set for tile as well. It's easy to install too.
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