Realizing it is over half a year ago you asked this, but since it does not have an accepted answer yet:
I ran into this very same issue over and over, and got fed up with it, so I decided to have a go at writing a script that displays console messages in HTML, so you can just view everything in the webpage itself, without having to resort to a console-replacement or a tedious remote debugger (for which you, indeed, require a Mac), without having to modify each console call in existing code.
The key lies in 'replacing' the four main functions in window.console: log, warn, error and trace. This is done by redifining each method, adding own code to that, and calling the original method in the end. Jakub Fiala wrote the basic script for that, on which I built the rest: https://gist.github.com/jakubfiala/8fe3461ab6508f46003d
I dubbed it 'MobileConsole'. It is quite unobtrusive and will 'catch' all console.log (or .warn, .error or .trace) events, and even bind to window.onerror.
I have created a separate page for this script with an elaborate explanation on how it works, including a demo, over here.