I'm taking out 5/16 parquet and installing 3/4 x 3 1/4 hardwood strips w/ 2 in cleats. In taking out the parquet some of the subfloor is coming up too. With these gouges and the leftover adhesive, it makes for a pretty rough surface for laying new hardwood.

The subfloor is 1/2 in plywood over another 1/2 in ply. I can take it out and put in new, but that's a lot of work (especially after removing 330 sf of parquet!) I'm wondering if this is a situation where the self-leveling compounds might be of use.

I could also come back over the two half-inch plys with another 1/4, that that makes for some bigger transitions than I'd like. Likewise, leaving the parquet and going over the top of it doesn't seem too tenable.

Any suggestions? (I've already pulled up and replaced about 600 sf of particle board underlayment for two other carpeted rooms. My back wants a gentler solution. )

You can either sand your subfloor smooth and patch it where needed. Or replace that top layer of 1/2". Floor prep is where many cut corners but it is the foundation of the job. If done poorly, nothing else will make up for it.