>>2790912Bike speed is 80% aerodynamics, 20% tire rolling resistance and 5% everything else.
Changing gearing won't do anything unless you're currently spinning out your heaviest gear.
Absolutely the best speed gain per buck would be lowering your handlebars and putting aero bars on them. Then you can think about getting some slick tires. Putting drop bars on a frame meant for flat bars doesn't work, don't even bother researching it.
Next best thing (or first if you have the money) is getting a dedicated drop bar bike. A grabel bike will be 90+% as fast as a road bike if you put road tires on it and will give you more versatility if you ever decide to take it off road. If not, a road bike.