First of all, I don’t know why you put the Pope two tiers higher in your example honor scheme than Buddha As I see it, there were just as many lying cheats in that office as there were righteous ones.
Setting that aside, I also think that reputation would be a much better fitting name.
In this spirit I would suggest to adjust the scale: level 1 characters would start at zero and can go up or down from there. Positive values would represent a good reputation (famously honorable), and negative values represent a bad reputation. This could directly be translated into advantage or disadvantage depending on the situation. If you want to persuade the Samurai that you didn’t kill that guy, you gain advantage for positive reputation, and disadvantage for negative reputation. If you want to persuade a street thug to better tell you an important piece of information because you will gut his sorry ass otherwise, you gain advantage if you have bad reputation and disadvantage for good reputation.
So, my question would be why you decided for a system where you just limit the attribute score by the honor score? It just seems to punish the un-honorable and has no apparent benefits for honorable characters. Also, a possible build-around would be to invest heavily in deception instead of persuasion and just lie your way out of a bad situation.
The only benefit for honorable characters is the “leverage honor” rules option. However, giving a lot of advantage suffers from diminishing returns. Meaning if you compare no advantage with advantage 1, the expected result is about 2 higher for the advantage 1. If you compare advantage 5 to advantage 6, you have not even an improvement of 1. So, the advantage of having high honor is marginal at best in this case as well.