Don't pedal harder, change to another gear.

Your target RPM should be around 90-100RPM. I find that sometimes if I'm going at 88-90RPM at around 20mph, then downshift such that my RPM jumps up to 97 or so RPM, I'll boost my speed up to 21-22mph. Shifting up doesn't always mean you go faster.

You should actually be in the easiest gear that allows you to maintain speed. However if you feel any slack at the beginning of your down stroke, you're in too low of a gear and should upshift.