I think you should be upping your cadence? Spin more. I can cruise at 16-18 mph without using the outer gear at all. Unless the bike is absolute junk I don't think it would stop you from achieving your target cruising speed.

To go faster, I think you should use a lower gear, spin more, and don't start at top gear.

Edit: I should I clarify that I ride a regular bike, not a folding one although I am looking to get a folder in the future. But I still stand by my advice of increasing cadence, even if it means using a lower gear. I don't see how using a 3-speed would limit you to 12 mph, unless your bike has seriously low gearing.