Only 71 apiaries? My home apiary site is still on Beebase and it tells me there are 110 within 10k.
The info on their site is next to pointless.
There are terrain features to factor in, valleys, rivers, not to mention your neighbouring beekeepers and where they keep their bees and what bees. If these beekeepers are keen to improve local stock, you could form a small group and work to a common goal. Other association members interested? They can join in and your idea sounds less unachievable.
Associations should be encouraging more of this.
Incidentally, one site I was looking at quite favourably has 80 apiaries within 10k, supposedly. The area is a dead end, steep sided valley with one little village at the top of it. It's two miles down the valley to the next village or one little road takes you up on to the mountain top and it's miles to anything from there across remote moorland which certainly ain't bee territory. Where are these other apiaries? They are probably in adjacent valleys.
A circle on a map doesn't mean a lot.