I have 2 suggestions, I havent read through every post so I don't know if they have been suggested or not. They aren't necessarily just for free agency but here they are.
1. I would be in favor of a luxury tax for teams that go over the cap. Something like 5-10% above the cap with a 100% tax. If the cap is $80m, a team can go over that cap by $4m-$8m but they would also have to pay an addition $4m-$8m tax. I know I'll hear the "you only want this because it benefits your team" to which I'll just respond with "you only don't want this because it doesn't benefit your team". I don't think it would be like the MLB. Their cap is already ridiculously high and there are teams that literally employ individual players that make as much as entire teams which is not close to what would be the case in the NHL so saying that you don't want a "Yankees of the NHL" wouldn't be a legit concern.
2. Add "option" years to contracts. It doesn't have to be every contract but teams and players should be able to have option years in their contracts if it's agreed upon and written into the contract. This would stop teams from having to worry about locking up young players that might not pan out. It would stop players from signing long term deals and then dogging it. it would also allow young players to sign long term deals without worrying about outplaying the contract if they have the option to opt out and either become a FA or sign a new contract. If a team signs an older player to a 3 year deal, they can add an additional 2 years as a team option if he doesn't decline.