Planting a cool-season perennial grass, like orchardgrass (&/or fescue, which is what holds the world together in this part of the country) is best done in fall - like late August to October. Spring seeding is gonna be iffy... too hard to get into the fields at the right time to drill, and too much likelihood of getting into drought situations before the grass is established.
Depending upon thickness of stand and fertilization , you could probably get a cutting in May of the establishment year, and a second one later in the summer. Some folks would plant a thin 'nurse crop' of wheat at the same time, if planting into a prepared seedbed, but for my pastures/hayfields, I usually just no-till drilled a mix of Persist Orchardgrass and a novel-endophyte fescue, like Max-Q. My success drilling clover at the same time was poor - I think the NRCS rental drills planted it too deep, so I usually just overseed clovers/lespedeza in Feb and let frosts work the seed in. I understand that since you're managing this primarily for deer, you probably don't want fescue... but in a pasture for cows and horses... it's hard to beat, here in the 'Fescue Belt'.
With a well-established perennial grass/clover hayfield, I'd count on at least two cuttings per year, maybe 3, if fertilization is optimal and rainfalls are timely. No one in western KY is gonna be cutting hay every 28 days like somebody growing alfalfa in MN.
Orchardgrass does seem to thin/peter out after a few years, and will need to be reseeded periodically. Red clover, which the hay folks seem to prefer, is gonna mostly disappear after about 2 years. Ladino clover varieties will hang in there pretty good, so long as you keep soil pH right.