Where the fix? None of what you listed fixes anything.
Players need a way to interface with the game to indicate the plot they want to own. Remove placards and you've removed the ability to purchase altogether. No one gets anything. Nothing is fixed.
A lottery doesn't guarantee that a player who meets the requirements will get a house or even that anyone will (see below). Nothing is fixed.
Restricting mediums and larges to FCs means more players creating shell FCs so they can own one. Watch all the shell FCs for solo players now owning the mediums and larges while legitimate FCs can't get any housing at all because they're blocked from purchasing smalls. Nothing is fixed.
There aren't enough smalls for every player in the game. Nothing is fixed.
Taking away the excess houses from multiple house owners is a drop in the bucket compared to unmet demand. Nothing is fixed.
Increased plot costs makes it harder for players, especially those with only a few hours a week to play, to obtain a house while players with hundreds of millions of gil or lots of real life disposable income to spend aren't impacted in any measurable way. Nothing is fixed.
Before you can suggest any fixes, you need to identify the real problem The real problem is the lack of a dynamic supply able to meet the demands of a player base that is continuing to grow (which is pretty rare in a MMO that's 7+ years old) but is growing at variable rates on different worlds in different regions. We're stuck with a static supply that is the same for every world despite population imbalances and that does not automatically grow as the player base grows.
If you want to fix the problem, you need to create a dynamic supply system. Other MMOs have it - it's instanced housing. It's worked very successfully for them. Players aren't limited to one per account, or one per world, or one per character. Players can get as many houses as they want.
Let's stop suggesting that SE waste their time making torn bandages that don't fix anything and start requesting they use their time to create a real solution.
That's not how lotteries work. With a lottery, participants pick numbers. Then a winning number is independently picked. If no participant picked the winning number, no one wins.
You really want to see plots sit vacant for weeks because no one manages to pick the winning number?
If you want plot ownership based on RNG, you should suggest a raffle where participants are given numbered tickets and a winner is drawn from the tickets given out.
It still doesn't fix anything.