I feel like I posted this elsewhere, but assuming you want to keep both goals, I think there should be a lottery carryover system. So similar system (flatter odds, lottery for 1-4, playoffs mean you get no lottery balls) but if you don't "win the lottery" you get to keep your lottery chances for the next season you're in the lottery. If you win any of the lottery picks, you lose those chances. And that should stack for multiple seasons (probably with some type of 3-5 year cap. So with a 5 year cap, if the Jazz were the worst team again next season, they'd be looking at around a 40% chance for each lottery draw (14+14+4+4). With multiple lottery picks in one year, the second you win a lottery pick, that extra advantage disappears.
Biggest issue here is how to grandfather it in.