Although the idea of some "lost" teachings of Kahless being rediscovered is intruiging, it's a bit too close to "Kir'Shara". Nothing against those episodes. I actually really liked them, but been there, done that.
Setting aside whether one considers ST:O canon or not, I could see a greater emphasis on honor under Martok. Given his own humble background, I could also see him less concern with maintaining aristocratic traditions and being more open to appointing those from a "common" standing to important positions (assuming a chancellor has the authority to do that).
If the Empire is prosperous under his rule, it might make it easier for more progressive Klingons to gain support.