Yes, I believe the mirrors were there to help everyone see himself.
The Scriptures may steer us, but as you say, they are not enough. The human mind also needs to be changed so we can see correctly. If we can't see ourselves correctly, is it safe to try to approach the holy? Is it even possible?
Romans 12:1 I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service.
2 And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.
It is possible to try to approach the holy with the wrong attitude as two sons of Aaron attempted. Too much effort along that line can be dangerous.
This thing of striving ourselves is good and expected... but it is NOT enough. The verses you quoted tell it if we can understand them. To me they mean for us to surrender completely to God, so that as we give it all we have, He will take up all necessary slack. The surrender is not a one time thing. Today I may surrender to God, but then come morning it is today again and I am back in the driver's seat. But... I cannot drive this vehicle along this route on my own. Surrender the seat again to Him. How many times? How often? When is it we will by doing this be transformed and when will we have proven the good, acceptable and perfect will of God? When can we say truthfully that which Paul said here?
"I have fought a good fight, I have finished my course, I have kept the faith:" II Tim 4:7