Have you considered using the Rounds by building a square bale form, dismantling the round and tying your own square bales for use.
making a hand bailer
Last year we got lucky and found a farmer that sells straw and hay, he makes both Rounds and square bales, so we now have a year round source for square bales of both straw and hay.
We do buy many from him since our hogs eat the hay in the winter once all their greenery is finished. We use the straw for bale gardening, mulching and hog and dog bedding since our supplier uses no chemicals on his fields. (again we are lucky).
I found the hand bailer easy to build and it works a treat.
The best tip is to use two people when you are ready to tie off the new square bale.
I made ours to the dimensions of a machine made square bale (24" x 32" x 48")
I should have made it so the bales were only 36" when full to the top, it would have made handling the finished bales a lot easier on my old body.
To tie off make a loop knot in one end then you can feed the other end through and pull back to make the bale really tight, a couple of half hitches will hold until you can tie a millers knot right behind the half hitches.