I used to grow hay, so I get the challenges of mowing on time with just weather as your obstacle. With weather and only odd days to do it is just plain tough. Finding a responsible neighbor is always a challenge. If it were me, I would think of trying a slightly different approach.
You could get a few cows to graze down the paddocks between horse use...buy young, sell older, and you would still be earning money that you are missing by not haying.
Depending on how soon you want it for horses, if I were trying to build fertility for horse use in the future, I would think about green manuring it by planting pigeon pea or similar crop and tilling it in, and repeating.
Even just doing rotational intense grazing with cows will build soil fertility quickly.
All the best,
Peter