[dice]

You could do a test: take a small section and just put a foot
of mulch on it over the winter; take another small section
and grow a thickly seeded winter cover crop on it (half and
half winter rye and hairy vetch, for example, or whatever
is recommended in your part of the country for that, with
maybe an inch of compost on top of broadcast seeds);
cultivate the rest with your original plan.

Then turn over a few shovels full in mid-spring and compare
the soils. The thick mulch helps natural processes form
aggregates in the soil with larger air spaces between them
than smaller particles of either clay or humus. The cover
crop fills the soil with roots. Grow a couple of plants next
year in the test sections and compare their performance
to those in the fall-cultivated bed.

Adding gypsum or lime, depending on pH, will also help
improve the structure of clay soils. (One should get a soil
test first, to see if it really needs more calcium.)