JusticeZero

One: Gearing. On my bent (not totally the same comparison I know, but it started out as a mountain bike, a Trek y-26 to be exact.) I switched out the cranks for road cranks. It won't actually help your speed directly but it'll give you a bit more room on top, and if you're doing most of your riding at the top end, you may be wanting to dial it up or down for conditions a bit more than you can when you're stuck at the top end. Readjusting to the new gearing would also help you with..
Two: Cadence. yeah, it 'feels like you're in a granny gear'. Do it anyways. =) You do better at a higher cadence. You'll get used to it soon enough.
Three: Pedals. What kind of pedals do you use? I have some aggressive platforms, and I can pull on them to some extent. Clipless is, alas, not an option for me. Keep working on spinning the pedals in circles and lift up on your foot when it's not pushing. No sense losing the power from your wheels that it takes to pick your leg up when you can do it yourself.
Four: Tires. You mentioned getting some better tires, and others have commented on it already.
Five: Handlebars/aero. Are you riding upright? Maybe if you got some positions that dropped you down out of the wind a bit more you might pick up some speed. if that's not comfortable or just plain annoying that's fine, but there's a reason they have those superman bars on fast bikes. If you really have a 'need for speed', eventually you're going to need to get a road bike for that reason. Or a recumbent.