All the services I've used (Strava, Google Maps, Bing Maps) seem to be essentially the same. They're route planners, so they want to plan your route for you. When you have a specific route you want to follow, that inevitably means you have to drag the route back to where you actually want to ride, rather than what the software thinks is the shortest, fastest, safest or whatever.
Remember that the software tries to find the best route between waypoints. That means that the most efficient way to correct it is to find a large segment that's strayed from your desired route, and drag the middle of that segment back to the correct place. Also, it sounds like your intended route is "just ride along the towpath" so you don't need directions along the ride. In that case, you don't really need to correct every single deviation from your intended route: a 10% error won't make much difference to your trip.
Strava's map knows where the Oxford Canal is and knows about its towpath. Just now, it took me maybe ten minutes to plot the 60km from Rugby to Banbury, being fairly careful to follow the canal. A further advantage of Strava is that you can upload the route to your GPS device or follow it on your phone. Strava requires you to create an account to edit routes and so on, but I've not had any spam from them or anyone else on the email address I gave them. For route planning, you need to use the Strava website, rather than the mobile app.