If you can fix the battery, it would be a nice bike. It's also possible to tweak the controller for better hill-climbing, but only with a good battery.
With electric only at 'legal speed' you have managed to cover the full commute distance one way, so with some peddling you should be comfortably made the journey one way on a charge. I suspect you could get 20miles easily with peddling at this speed, although taking 1hr40 to get to work isn't ideal.
I have a S-pedelec Bosch 11Ah battery and if I use full power would drain the battery for a full commute of 38 miles with lots of peddling (albeit at slightly higher speed). Not sure whether your battery is that bad actually. Just IMHO of course.