Thank you! I've since removed admintools since I woke up to both to your email and locked myself out using a caching program on Siteground
I've also just subscribed to your web based system to check it out further. The first 500 URL's I saw had all the https URL's I was hoping for.
FYI, the problem was with the admintools software! After I deleted it, it's been running the HTTPS URL's almost fine although I keep seeing weird extra hostname URL's like:
[external links are visible to admins only] but I suspect it's a Joomla misconfiguration that I haven't figured out yet.
Best 'net regards,