I think this would go a long way towards helping out parity while helping protect the players against cap inflation, do away with frontloading and backloading. Don't change anything with respect to contract duration.

Still keep the supermax at 35%, the regular max at... say 25% + an additional % for every 3 years' experience, etc. The minimum salary would be 1% of the cap and teams would only be allowed to sign 1% contracts when they're over the salary cap. Every team gets a MLE or RE ranging from 5-9% of the cap and teams can only have one Larry Bird exception re-sign player per season, up to 15%, and a hard cap at say, 120% of the salary cap.