Thanks for asking; I've been meaning to write a followup post here to share my experiences.
To start off with, the weekend after I posted it rained non-stop for 3 days here, and there was mold on my wheat. Upon researching, it was the variety known as Sooty Black Mold, which in almost all cases is both superficial and unavoidable, especially with the high rain and humidity we've had in the area this year. While it was startling to see mold on 60% of my crop, 2 days after the rain stopped it had all cleared up and there was no visible damage to the wheat grains themselves.
I should have threshed earlier, as I lost a some wheat to shattering and my own improper use of a scythe. Practical experience with tools and equipment is the best way to learn and towards the end of the patch I had a good technique down. The grain was fully dry within a few days of being in a shock; it was between 5 and 10% moisture, which is perfect for storage.
Here's where things go bad: while threshing, I noticed that 1-2% of my grains were pink or white and a little fuzzy. I was unable to winnow these grains out using a box fan set on high, also. Turns out this is the result of a disease known as Fusarium Head Blight. This stuff does damage grains, and can produce a toxin that is harmful to humans and livestock in pretty small quantities. The maximum limit set by (I believe?) the USDA or FDA is one part per million. This disease is spread by planting in infected soils, contact with infected plant material left in a field, and probably the fact that mold and fungus spores are everywhere at all times.
I contacted the state extension service but have not received a reply on what I can do about this. From my own research, and the fact that I am personally sensitive to mold, I have decided to stop processing the crop and call it a failure. It isn't worth risking my health or well-being for 100 pounds of wheat, at best.
I did learn that both Fusarium Head Blight and Black Sooty Mold are also caused by high rain or humidity during the heading stage of the wheat; in this case, June, when we got something like 7" of rain in a few weeks. Perfect breeding ground for such problems, especially as I did not spray with fungicide or any other treatment.
One other symptom of Fusarium blight that I noticed was that it causes infected plants to turn gold and die a lot sooner than the rest of the plants. I didn't know that's what it was at the time, but if you grow wheat and see heads dying very early, that could be a warning sign for you.
If anyone knows any good ways of removing the infected grains, let me know. I know there are tests you can get done to the grain, but I'm also nearing the limits of how much I can spend on this
project this year. The good news is that I'm more prepared for next year, as everything that I had control over was successful.
EDIT: for anyone who wants it, this is a helpful publication I found from the UW Extension office:
https://fyi.uwex.edu/fieldcroppathology/files/2010/11/Wheat_Disease_ID.pdf