The rod not having free travel could very well be the problem. Another thing to check would be the seats in the master cylinder, the place the flare nuts on your brake lines screw in. If by chance it's a drum brake m/c then there are residual pressure valves built into these seats--something you don't want with discs if your cylinder is high mounted. Even a low mount cylinder with discs only uses a 2# valve so a 10# drum brake valve will make discs drag.

Evan