On the very rare off-chance that anyone has a similar need, I just thought I'd post an outcome to my original search for a good Events Registration/Online Booking and Payment software with a SQL backend. I eventually tracked down a very good product (not sure if we will buy it, but that's not my decision). Evocos from Silverbear (www.silverbear.com). Ticks so many boxes for us, has a SQL backend (rare as most are SaaS), is flexible, and the interactions we have had with their staff have been very professional. Very impressed with them.

Bex