You might want to check out the trp spyre brake units, they actuate from both sides, like a hydraulic brake, but are mechanical. I have avid bb7 on my gravel bike and when I upgradez I’m going with the trp as I want to keep the simplicity of the mechanical but improve the feel and performance.
You could also get a larger diameter rotor. 203 mm rotor on a road bike, ftw.
And putting the front brake, where the real braking power is at, being operated by your stronger hand, is a good idea.
I wnet from shimano mechanical, to Tektro mechanical, to TRP HyRd, a good improvement everytime.