Communication through MozRepl is a bottleneck for WWW::Mechanize::Firefox which significantly limits real-time performance.

If I were you, I would use WMF to inject a JS-Routine to do the website loading and log start and end (needs definition) and calculate the difference.

Use WMF to poll the logged data from the perl-side.

Tip: I'm simply setting window.title for that purpose, it gives visual feedback in the window frame and there is a ->title method in WMF to read that field from perl.