I'm gonna keep this post short, sweet and to the point.
Also, as crazy as some of these ideas are, I'm actually being serious. Sometimes the best option is the craziest one, like that saying, "it's so crazy it just might work".
Here are the possible solutions to fix the draft:
1. You make it into a wheel.
2. You make it into a tourney. One and done format. Lesser teams get the homecourt. The two worst teams automatically advance to the 2nd round. The matchups are decided by order of closest competition until the Finals obviously. What that does is guarantee one really bad team the #2 pick at worst and one borderline playoff team the #1 pick at best. Then like the Olympics, losers continue to compete for the next best pick. It'd take one week for this tourney to carry out. It'd increase the revenue of the NBA as well as force teams to compete during the season. This is my idea:)
3. Every team gets one lottery ball which means every team has the same chance at getting the #1 pick.
4. Players choose where they want to play and teams have the right to accept or decline their application.
5. Teams with the best free throw shooting % get the best picks. It rewards teams who can execute the simplest play in all of sports. This system not only makes it fair for everyone, but helps make players and teams better by forcing them to practice their freakin' free throws. As a consequence it also makes every single free throw that much more stressful for fans like me and you. My other idea:)
6. This game has many names, but in my school they called it "speed". Two basketballs, people lineup and you have to score as quickly as possible. If the guy next in line scores before you do, you're out. Every franchise sends one person to this game. They all wear the jersey of their franchise and they all wear masks to keep themselves anonymous, thus protecting themselves from crazy fans like me and you. I'll take credit for this idea too.
7. Other (you list)
I know I didn't go into great detail in these, but that's what discussion is for.