I have been doing a bit of research on this and have tried one test, like you.
We tried growing hard summer wheat several summers ago. I forget what the name of the seed was but it was a heirloom type typically grown in New England in the 1700 & 1800's.
The land we planted on was a former pasture reclaimed from a stand of pine. The land had a gentle slope north to south. It was a bit rocky however most land in the NE is rocky. The size of the plot was ~1/3 acre.
The land was plowed to about a 10" depth then roller disked. We did not have a seeder so we scattered the seed by hand then ran the disker back over it to help "seat" the seed.
The seed sprouted within 14 days and we were all rather proud of work. We all had visions of of bushels of whet neatly stacked in the field slowly drying in October. I even went out and purchased a sickle bar mower.
As the weeks past, weeds started to overtake the plot and stunted the growth of the wheat. In the end, there was wheat but it was so mixed in with weeds, we never harvested the end product. We then turned the cattle in on the field for them to eat and fertilize.
Further research suggested that we should have not planted spring wheat but winter wheat in the fall for a spring harvest. Apparently a winter wheat field will curtail the proliferation of weeds as we experienced with the summer wheat. We also learned that the winter wheat is less vulnerable to pests.
We did not try the winter wheat this past fall. We just ran out of time with all that was on our plates. Maybe next year.