We did this years ago at my dads, make hay by turning as usual, we then rowed it up and borrowed a buck rake for the back of the tractor. Reversed up the rows and drove it to the barn, forked it up as high as we could. In the old days they used hay sweeps, essentially huge buck rakes, useable because hay is so light, but you don't see many around these days.
Baling rates aren't that dear, do you have any vintage enthusiasts in your area, you might able to get someone to bale it.