You don't need to know for sure that a team is losing on purpose in order to give them incentive to win more. You just need to make it worth their while to win even when they don't have a chance of contending, or even making the playoffs. I'm not saying I have a better solution than Bill's ridiculous tourney, but I do think that something ought to be done.
Well, if a horrible team is actually trying its hardest to win games, no incentive can make the team win more.
I just think you're trying to do the impossible. As long as win-loss affects draft position, teams will always have incentive to tank. You basically have two scenarios. You can either have there be more incentive to tank, meaning that truly bad teams have more hope of improving, or you have less incentive to lose on purpose, at the cost of those bad teams having less of a chance of getting better. It's like saying you want lower taxes and more government services.
There will be meaningless regular-season games. There will be bad teams. There will be hopeless teams that are a few seasons from being relevant. Hard cap, soft cap, guaranteed contracts, unguaranteed contracts. It doesn't matter. If you really want to change the competitive balance of the league, think about changing the structure of the season or the rules of the game.
Anyways, if I wanted to do something like that stupid Simmons tournament, it wouldn't be for the last playoff spot and a draft pick, it would be for extra cap exceptions. (Keep in mind, I am a proponent of keeping the soft cap, so exceptions still play a role in my proposed future.)