Your changes indeed speed things up on my testing system so long as they don't cause additional swapping. I see only one issue. It does seem to use more memory than the stock LWP::Protocol.

Yours hit more heavily into my swap file for a large file (703MB on a system with only 512 MB of RAM) than the stock version. The map in BrowserUk's version put my poor antiquated testing server right out of physical RAM and swap completely.

My conclusion is that I really do need more RAM in this machine. It's something to consider if you're under similar constraints or if you're submitting a patch to the module's maintainers, though. As always, paging to swap can erase any gains you'd get otherwise and then cause even much slower execution. Sometimes optimizing for speed at the expense of memory fails, and sometimes optimizing for memory use is actually a performance win.