I've only just found the Haysom site on the Genealogy website and have enjoyed reading all the many emails from various Haysoms!
Maybe you've stopped doing this now, as some of theseemails go back to 2001. However, if you're still out there (!), I just wanted to say my mother was a Haysom and comes from the Hants connection. I know her grandfather, William, was a schoolmaster in Pennington , near Lymington and my grandfather, Harry, was born there ( not sure of the date ..prob 1880s ). He was one of about 10 children I believe and I know quite a few emigrated to South Africa. ( As did Harry, but after his death, the family returned to England) .
When my parents retired, ( 1981), they moved to Swanage and we always knew there were Haysoms there. We found cousins living in Langton Matravers. One, Trevor, is still a quarryman ( this trade goes back a long way in the family I believe ). He has a sister also living near by and his father was Walter.
There are quite a lot of Haysoms on the "Swanage Burial" website I found by chance on Google. The family goes back to 1700s.
If you have more detailed information on the Hants Haysoms, I would be very grateful if you could send it to me.