I don't know about loading a GPX onto Google Maps in a way that you can see "live" where you are, but if you can upload your GPX file where it can be accessed via a standard "http://" URL (obviously ending in ".gpx"), you can feed that URL to Google Maps as its "location" and it will display the route.

Secondly, I set my Edge 705 not to auto-reroute. I find that the auto-reroute loses my original route if I go off-route. That's a problem because even if I backtrack to where I went off-route, it may no longer have my original, carefully planned route that avoided the busy roads. With auto-rerouting turned off, I can still see where I am relative to where I was supposed to be—even if I was obliged to detour by some roadblock—so I at least have some chance of "manually" navigating back (or forward) to where I can resume my route.

Other problems I've run into with my Garmin: If the route has lots of successive, closely spaced turns, it can fail to keep up with your actual location and lose track of where you are. If you have a route that backtracks along the same road/path later on, it can get confused about whether you're outbound or inbound and start directing you to "make a U turn". I avoid that by splitting such routes into separate sub-routes.

From everything I've seen to date, dedicated bike GPS units still have much better battery life than smartphones actively using GPS. You can get around it with external battery power, though, at the cost of added weight.