If you have not already done so a 2 minute visit containing 5 minutes of smiles wrapping a jar or two of your honey with a short "B" lesson might get a foothold into the back of the mowers mind come next year.
The first time we extracted honey, we had bees in a residential neighborhood, and I took a bottle of honey to all of the neighbors that spent the summer tending nice looking flower gardens. The conversation started with 'I am returning some of your flowers', and handed them a bottle of honey. The next spring, a few of them were asking what to plant for the bees, to get a larger honey crop.
Go talk to folks with a smile, and a bottle of honey. Between now and next spring, every time they hear some dramatic news clip about honeybee die offs, they will remember that conversation, and it will re-inforce that conversation. By next year, you may well be pleasantly surprised, and if there are no overriding reasons to force that cutting schedule, do not be at all surprised if they come over and ask you, 'when is the best time to cut?'. I've seen it, happened to us already with one lot right behind us in our new location after we moved.