I need help creating a new kind of duration modifier

In essence I want a plugin that will create these:
https://ianring.com/stardots/

The syntax of the stardot is almost the same as an augmentation dot. Instead of increasing the duration by 3/2, it increases the duration by 5/4.

I've scoured the documentation looking for a way to do this, and there seem to be no convenient methods available to plugins. The closest I've come is to create a Staff Text element with the star glyph, which ends up positioned above the note, not beside its notehead.

Also I've had no success with changing the "tickLen" property of a note to make it span a longer duration.

In an ideal plugin, I'd be able to add a stardot to any note, and the star would be attached to that note; and the star would adjust itself up and down automatically as a note's pitch is edited, just like a regular dot does. I'd also like a star to appear in the note palette too, alongside the other augmentation dots. I get that those features might not be possible, but one can dream.

For the sake of staying on topic, please don't drop comments explaining why I should use ties. I'm looking for a way to do this notation in Musescore, not a discussion about whether you personally think it's legitimate.

I'm looking for a plugin-based solution, that isn't manually adding the glyphs and making invisible rests.