This won't help with logging as you mentioned, but for debugging you could try this on Linux:
nc -v -l -p 3000
Then you send the request to "http://localhost:3000" , or to your server's hostname if it's not on localhost.
This will show the entire request. You need to Ctrl-C out of it.
Google took me to this page for showing the full request headers with LWP::UserAgent and this was the actual answer I used.