People, people, people, have you not read your Dickens, or your O. Henry? In your attempts to find an answer to the chaos, you've overlooked the obvious: the answer IS the chaos.
The solution lies in digging further. Make the system so overwhelmingly complicated and frustrating that the only people who could ever stand a chance of making their way through the gauntlet are those who are truly willing to forsake everything they hold dear in their quest for their tag, and as such, the only ones who deserve them.
There's lots that can be done. Starting with the following ideas would whittle those numbers down real quick:
Squaring points? Go all in and y=mx+b those points. You don't just need points, you need point rates.
Looking up last year's draw results? Try no draw results from the last 4 years.
How about implementing Russian-style sale of tags and licenses? Anyone who isn't familiar with such a system, it's an arduous, long-lasting process where you have to identify and purchase things without much of the information you'd like to use, and you are not allowed to ask questions or for help. I remember how difficult it was to buy movie tickets in such a culture, getting a hunting license, tag, points, and all other sorts of things would be a likely impossible endeavor.
Make points only available for purchase on site, in person, at some government building somewhere in some obscure location in the building. And do that thing where the building you have to go to doesn't make any sense, like the Revenue or Department of Administration buildings (inspired by Montana sending you to the local county treasurer's office to do car title work).
Add nonsense paperwork. Forms on forms on forms. You can't just buy preference points, there's a whole procedure involved! What, you didn't bring a D182-C? Well, back to the line you go - next!
Anyway, there's a start. Anyone who can make it through all that deserves a point. Most of us would give up at the Russian-style koisk where they won't tell us what kind of tags we can get or how much anything costs.