I'm confused on why you see this as more of a speed issue than an endurance issue.
True. I referred to speed but might as well have mentioned endurance. Probably because endurance (i.e. more hours in the saddle) is the first thing that comes to mind when figuring out how to cover more ground in a day, and while there are certainly questions to ask (how many hours is too many, i.e. preventing recovery), the principle is fairly straightforward compared to power (is it reasonable to expect a meaningful power increase thru casual training, and how to do it best)
So let me say that at the moment I am trying to see if power can be improved by training. My tentative answer after a few days is that it is very likely -- I've raised my cadence from 65 to 80+ and unless I pedal with correspondingly less force, that should mean more power, i.e. more distance per hour.