There's no way to solve the Helga/Meloni puzzle without a wish.
And the save file thing is a limitation of HTML and Twine, so it will be always tied to your browser cache, unfortunately.
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I'm by no means an expert on Twine or HTML, but, within Harlowe (the Twine coding language I'm using), the save options are limited to the browser cache. It's entirely possible that other games are able to do a hard save using Sugarcube or some other Twine language. I don't know enough about those languages to confirm or refute, though.