Thank you everyone for your kind responses. I have checked out all your links and I'm still having trouble.
I have refined my requirements a bit, in as much detail as I can muster...
- 8 by 4 inches
- double-sided
- pad-per-hole (any shape pads will be fine, although square is marginally preferable)
- plated-thru-hole doesn't matter
- no ground plane
I need this shipped to England, but there's no rush.
Again, I'm grateful for everyone's patience with this disorganised Brit's random requirements.
I never imagined that hardest part of electronics is actually sourcing parts! This makes designing curcuits feel easy!

Regarding the "putting 2 single-sided stripboards back to back"... I think in doing so, the combined thicknesses will be too deep for my SIP socket pins to reach through to the far side of copper. The boards I have seen are 1.6mm thick including copper.
Plus the two boards would have to have opposing strip orientation for the same aspect ratio.
It never rains...
I'm starting to think it would be worth using up a whole weekend just doing it the hard way and p2p wire wrapping all the pins on a bit of bare perf. The horror!