I want to ride faster

[TsPoet]

My average speed now is about 14-15 mph, (ok.....13 mph with a strong headwind!). I'd like to be able to go 18-20 mph.

Colleen

For reference (from someone who has both, sort of)
On my 20" front wheel bent (the recumbent equivalent to your hybrid DF), I average ~13 mph on my commute to work. On my performance bent (equivalent to an entry level road bike), I average ~17 mph on my commute to work.
Differences: aerodynamics, weight (32 lbs vs 25 lbs, bents are heavy) - that's pretty much it, I have narrow tires on both. My faster bent is also aluminum, which I think works well for me, and the other is cromoly. The weight difference is more than that, though - I carry cloths and lunch and things with me on the comfortable bike and much less on the road bike.
You should always buy a new bike when you want to! OK, my comfort bent is for sale, I've run out of room to store them all.