No, you can't pay for placement. Please search the forum for advice on promoting your games. People ask all the time.

After glancing at your game descriptions, the obvious tipp to promote your games on Itch specifically is to have a project that has content that is not behind a 20 bucks paywall.

The problem is, that Itch has no try before you buy. Refunds are possible in some situations, but are for the extreme situations and not for buyers remorse. Steam has a two hours refund no questions asked system, so there is less risk to buy from a dev that you do not know.

A "public version" as I know the term is a free version, not a demo version and also not a paid version. It might have a pay what you want button and gets released later than a patreon version, but it is for the general public and not the selected group of paying customers. Your latest two comments on that slug game display the situation very well. You need to have a demo on Itch while it is being developed, not after the fact when it is done. People like to accompany the creation of a game. And you need to be specific about what people will get, should they donate/buy here - should you set up a project with a pay what you want button.

Since you are on Steam you are bound by their terms. So no public version. But you can create a downsized free version. And of course you can add a demo on your paid game project page.

As for search "optimisation", remove the clutter from your game's titles. As I said, it is literal search. Every word in your title that is not the title lessens the relevancy overall of the other words. You can put the clutter in the short description that shows up below the title.