Here is my idea
The teams 1-13 Get 30 balls, Teams 14-30 each get 20 balls.
Starting with the first pick, one ball is taken, they get first pick. That winners balls get removed and the next slot is picked, so on and so forth to last pick.
A playoff team has a 2.7% chance of winning the first pick even if they finish with best record and the bad teams have a 4.1% chance.Nobody is tanking with that system.
Another version is you could give worst to first that amount of balls, so worst gets 30, 2nd gets 29 all the way down to 1.....Still be significantly less tanking with that format.