You have really asked two not-quite-related questions.
Your relative slowness is probably not inherent to your 18" wheels. But it may be inherent to other aspects of your bike.
Note that the Moulton still has a world speed record, and riders using BF pocket rocket pros or Air Glides are able to achieve results that are very very close to those reached by riders using nonfolding road/racing bikes. This wouldn't be possible if there were something inherently slow about the wheels.
However, the bikes mentioned above are both very lightweight, have an aerodynamic cockpit with drop bars, etc., and have gears appropriate for racing.
Rohloff equipped Birdies weigh 28 lbs, IME have a fairly upright riding position, and don't have racing-appropriate gears.
So you may want to consider using a road bike the next time, but the reason to do so would be for the other advantages inherent in the design, not just because they have 700c wheels.
Although what you should *really* do is spend $4,000+ on a dura-ace equipped
PR Pro, or maybe more on a Moulton, and ride that.
(It is also possible that you are slower than the other riders for reasons unrelated to your bike :@).