I'm getting a little ahead of my skis here, I don't even know what "N bioavailability" means. Most of my info is from talking to and reading stuff written by Randy Rodgers, who was the lead small game and upland biologist for Kansas for a very long time. From him and from my personal experience of hunting in Kansas since about 1980, here's what I know. The Dakotas are surely different.
In Kansas, peak hatch is said to be approximately June 10. In the southern part of the state, wheat harvest is well under way by then. Not so much as you go farther north, but every year is different. A late wheat harvest is a good thing for the Kansas pheasant hatch, as long as it wasn't too cool or wet.
Wheat stubble is much shorter than it used to be, which is a combination of newer varieties and cutting height. Some of it isn't much taller than your ankle. It used to come up to maybe the top of your shin or just below the knee. The only wheat stubble I've seen that tall lately has been cut with a stripper header. Lower cutting height=greater chance of nest destruction and hen mortality from the combine. Lower cutting height also reduces the cover available for any nests or broods that survive harvest.
It's sprayed for weeds soon after being cut. We all know that weeds=bugs=chick food.
KDPWT clearly understands the impact of wheat stubble. The Habitat First program offers to pay farmers for leaving stubble of at least a certain height, delaying spraying, leaving edges unsprayed, and/or not spraying at all. I'm not sure how well known, well funded, or popular it is, but it's on the website.
Randy Rodgers had an article in KDWPT's magazine many years ago titled "New Life for Wheat Fallow". It's still available. It advocated for modifications to crop rotation, tillage, spraying, etc. and claimed that the changes produced higher profits (not necessarily higher yields) and more pheasants. My conversations with him much more recently revealed that those recommendations wouldn't apply to the fields where I have some influence over farming practices. The article was about much more arid areas. Regardless, it was a great education on the relationship between pheasants and wheat stubble.
More recently, there was an academic paper about the use of cover crops by pheasants in Kansas. I'm not qualified to discuss the findings in depth, but one line in that paper stood out. The author described growing winter wheat as an "ecological trap" for pheasant nesting. Ie, it's great in April when nests are started, but by mid June it's not so good.