The JS in the page should attach an event to the link to append the new page at the bottom. Better: it should do it automatically when the scroll position is close enough to the end.
Bonus: the script should add a search box to search even in the content not yet in the page.
I googled if it's possible to intercept CTRL-F and handle it programmatically. It seems it is [1] but I don't know if I would do it: the user could be surprised to find a search box in a non standard position with a non standard behaviour. It reminds me of scrollbar hijacking.
[1] http://stackoverflow.com/questions/9159322/overriding-the-br...
What I would do is add a dialog the first time the user press CTRL+F. Asks if the user wants the default or the override. Save this in a cookie or in the database.
A simple (non-JS) "Search these comments" form would suffice, but I've never seen it implemented.
You have two option with the web. Either you put your logic in the backend or in the frontend.
This addition is obliviously to reduce the load on the server. So either you add some logic on the frontend to make the user experience good or you do like they do right now and have a bad user experience.