For ten years I had various guys cut and bale my fields and then I gave up and bought my own hay equipment. I'm sure conditions vary around the country, but around here no one does it for anything other than 100% of the hay, there's lots of fields and few guys still baling. People do it just to keep their fields mowed and keep the weeds down.
What I came to realize is that when you have someone hay your fields, your interests are fundamentally misaligned. How much hay a guy can take in a season is fundamentally determined by the weather. If your guy made as much hay as he could have due to the weather, but didn't get to your field, from his perspective he's not out anything. From your perspective you didn't get any hay, and your field never got cut and now you're going to have to mow it anyway to keep the weeds down. Part of this misalignment of interests is that the guy doing the baling is motivated to commit to any field that comes his way. If it's a dry season and he has lots of days of mowing, that means he never runs out. If it's a wet season, he's not out anything.
The other thing I've learned is that when it's a wet season, it's a wet season for everyone. So if your guy is too busy to get to you there's not going to be some other guy with free time.
For most people the limiting factor in haying is manpower. If you have lots of volunteers, I would consider getting hay equipment and doing it yourself. You can get old hay equipment pretty cheap, the reason it's cheap is not that it doesn't work, it's that the new equipment is so much less labor-intensive. Don't try to do it all at once, do a little bit every week over the whole summer. A schedule that would work here is every Thursday mow for a few hours after dinner. Fridays ted, and depending on how the drying is going, ted again on Saturday. On Sunday bale and rake, and put it up. Sunday is the only day you need more than one person, that's the day you have your crew picking up and stacking the bales. If you have 40 acres you could do 4 acres every week of the summer. That's really not very much if you have a bunch of helpers. If it rains between Thursday and Sunday just skip a week.