OK, the site has been switched to the new server and the base Customizr theme now works perfectly ... no noticeable delay compared to the child theme (with the getimagesize lines commented out).
For the record, the story went something like this ...
- live domain pointed to one server
- copy of the site was created on a second server (to become live server)
- hosts file on my PC was used to redirect the domain to the new server for testing
- getimagesize calls resulted in a 14 second delay in loading EVERY web page while in this configuration
- when the domain was switched to the new server, the getimagesize calls produced no delay at all.
The only conclusions I can draw are that getimagesize doesn't like non-local references (maybe someone with a better PHP background can confirm) or that the local environment got itself a little confused about how to resolve the url (the hosting package was bound to the domain name so it may have made certain assumptions when resolving domain names and the hosts file obviously wouldn't have come into play).
I hope this can help someone else that encounters the same problem :)