I've found the only way with seeds is to plant a few each in modules then plant them out, which is even more back breaking than planting sets. They do grow perfectly well though in groups of up to 5 and still keep their shape, although the group needs more space than a single plant.
I mainly use sets in a bed about 4' wide by 30' long - tiny by comparison to your area. It's my knees which really suffer so I wear knee pads and kneel on a board so as not to compact the soil unevenly - onions like firm soil and the board compacts it evenly as I work.
I really don't see an alternative to getting right down there and planting the sets one by one - which is probably why the person who has offered to buy your crop is happy to pay you to do the work.
Maybe it's worth getting a HelpXer to do the planting - they have strong backs and knees
On your scale getting in specialist equipment would be too expensive. I have no idea what machinery they use on a commercial scale, but there must be something. I don't know of any gadget designed for the kitchen gardener - it was probably the pot boy's job in the Victorian Kitchen Garden