Spread the seed out on a garage floor to less than a quarter inch thick. Add a couple fans for more air circulation. Add heat to lower humidity, if possible. It should dry in 24 hours.
If necessary, mix it with Milorganite, which will help dry it out. Should be spreadable.
I did a test.
https://www.lawnsite.com/threads/pre-germination-apply-wet.484328/
Wet seed can be spread using the water as the carrier. In water suspension it settles out quickly; it needs to be agitated almost continuously. I used a 2 gallon watering can. (OK, but this would be slow.) For a large field, I suggest use a short garden hose, from trash can or drum on a trailer. Siphon the seed in water suspension onto the ground. Attach a hose valve to control the flow--or better--just kink the hose to control the outflow of the seed slurry. Move the hose rapidly back and forth, to assure an even application of the flowing water slurry. Using a siphon, the flow is very low pressure, maybe 5 lbs psi. For faster flow you can use a larger hose--maybe an inch diameter. If you want to put your thumb over the stream to help spread the flow and throw the stream a little farther--so be it.
A sprayer could perhaps be used, but the slurry would probably clog the filter and pump quickly. Do not start the pump, Unless it is centrifugal. However if the sprayer had a drain valve--possibly the hose could be attached at that point. Your assistant walks behind and tries to soak every square inch of the prepared soil or turf. If no drain valve, just bring the hose out of the hatch cover and down to your applicator guy.
Do not siphon by mouth--fill the hose to start it.
Of course--any hydroseeding contractor would probably be happy to help you--and would have suitable equipment.
If you insist on using a spreader. Just fill it full of the water suspension of seed in water. I have not actually tried this. Watch out --it will leak fast. Should hold about 20 gallons. Break-thru agitator should work fine.
I don't know how much to mix--maybe a pound of seed per gallon.
Calibration--you are on your own. Do a couple plain water tests to establish the basic parameters. Wear boots.