And an update on the above reported issue - Tom was kind enough to provide me with ACP access, and I put a debugging version of the application in place, which revealed that the code from my script was running multiple times on each page, which it should not have been doing at all and doesn't do so on my test site. So, I took a look at my code and launched into improving it a little anyway.
Today, I put a new version up on Tom's site and it has resolved the original problem - no more delays being seen, no more multiple runs of the code. However, I am still seeing some weird behaviours with his quotes which I am not seeing in my own testing.
And then I spotted that Tom's quotes have 'Read more' at the base, and not 'Expand', so I took a look at his plugins and there is the old 'Minimized Quote' plugin that was needed prior to IPS 4.5. The delay behaviour being seen by Tom is actually due to the following:
My application's quote code running, which then tries to run the IPS quote code
The plugin's quote code actually replaces the IPS quote code and it is what is then run instead of the IPS quote code
My application then responds to what the plugin does, and runs again...and this cycle happens for each quote on a page.
Tom's sample page for me had 33 quotes on it...and the result is a delay which reports to the browser as a 'long-running script'
Problem solved - that plugin is now disabled on Tom's site and I will be testing out my new and improved version there tomorrow.
New version incoming soon.