I don't think you'll pickup 3mph just from switching to a roadbike.
Especially from a decent hybrid that you have right now. Maybe from
an older mountain bike you can make those gains. You can try renting
or road testing some roadbikes to make some comparisons.

I'm not saying this to discourage you from getting a roadie, just
letting you know what my experience have been. And from reading
other members stories, it seems they had the same experience.
You'll get faster as you ride more miles, this is true no matter what
kind of bike you're using.