I came across something I wasn't expecting. A free sale that has a demo yet somehow claiming gives the full version.
It's on sale for about another day https://coperun.itch.io/pixiffy
I don't know if claiming works there because there's two sets of files (Windows and Mac full versions + demos for both OSes), or what the reason is. From what I've seen on Itch I'm surprised it works.
I'm mentioning it in case you wanted to ask the dev how he set up that page so that claiming gives the full version. Maybe something he did there is the key to not having to do silly stuff like removing the demo during a free sale.
Edit: Hmm. There's a separate download button for each demo on that page, other than the download button for the full versions.
I don't remember if there was a separate download button for the demo of Some Little Adventures or not before the demo was hidden. If there wasn't a separate download button for the SLA demo, maybe that has something to do with it.