In my field I lay about that every year over the beds and it packs down to about a 2" matt by the next spring. The hops will grow right through it as they emerge so you do not have to cover them unless you want to.
It will be a mess near the top. Not really a big deal as long as you keep the varieties separate you are going to cut the top off anyhow for harvest. They might go the full 23" but doubt it.
Here is the current list
CASCADE 3.50 EA OR 4/10
CHINOOK 4 EA
CENTENAL 4 EA SOLD OUT
GLACIER 4 EA
HALLERTAU 4EA
MAGNUM 4EA
GOLDING 4 EA
TETNAG 4EA
FUGGLE 4EA SOLD OUT
WILLIIMETTE 4 EA