OK, an update....
I decided to go with phpBB for the new software. However, I dont want to leave the old boards locked and available. Previous problems appear to have been exaggerated by 'guest swarms' and a locked read-only board is just as vulnerable to them. Also, there is no converter from IkonForums to phpBB. But... there is a convert from Ikon
Board to SMF, and a converter from SMF to phpBB.
So, I have run the IkonBoard converter to SMF and this is now partially (mostly) up and running. It took a while to convert over seventeen thousand threads

and we have lost around 80 threads in total somewhere (whether these are really lost, were duplicates or never existed in the first place is open to interpretation - and considering I wasnt expecting much from a converter that isnt designed for that particular platform, I am not unhappy) and - of course - the attachments are floating and not connected, although I still have all of these as I will keep the old installation available for myself only.
Next stage is now to convert from SMF to phpBB, give the entire thing a quick once-over check and open it up. It will be a couple of days, but there is a light at the end of the tunnel.
Thanks for your patience.