Your setup sounds great and should work out really well.
If you are using big box cow manure, don't add any more sand.
If it were me, I would back pedal, I would remove the soil less medium.
Dig out about 6-10" of the native soil, set aside, fill with old rotten wood, mainly logs, wood with fungi work great, then branches, then twigs, fill large voids with "pine bark" mulch and similar media, toss in some of the native dirt you removed, then any other yard waste, ashes, bio-char, kitchen scraps, shredded cardboard, shredded paper, pizza boxes, TP rolls, etc...,toss in some straw, more native soil, some of your soil less medium, and keep layering and mixing between your native soil and your soil less medium, top with at least 4" of your soil less mix.
Make sure to soak each layer.
Sounds like a lot, but you can do a section at a time.
At the end of the season, chop and drop, top with yard waste, add a bit of Manure and/or compost, plant Oats and crimson clover, and start in situ composing.
This bed design should help retain water and self fertilize.
Nitrogen tie up should not be a problem your first year if you top with compost and manure.
Also using the pine bark mulch will not tie up nitrogen like wood chips do.
In the years to come you will be glad you took this extra step.
However if you want to plant out this year, use the beds as is, start collecting your materials and start this in the fall, maybe doing one section of the bed each season.