I rode with a brake for four years before I rode brakeless.

If you really insist on riding brakeless at this point in your riding (not advisable) get a bigger cog, like a 19 tooth cog, and, although you won't go as fast, your skills will improve quickly.

By the way, I like your use of the phrase "pedal pacing."

I've not heard that phrase used before.

I ride at 63 gear inches, way to low for most people on this forum, but I've learned to spin (and go fast by spinning), and I can stop without skidding (I pedal pace).

I also make a point of not going down hill any faster than I can go up on the same hill.

Even with those constraints, I average 15mph on trips around town, including stop lights.

Four minute mile.