Need help with interesting musical experimentation

I'm trying to do something with MuseScore that I'm not sure is possible, and I'd appreciate some help trying to figure out a creative way to do this using MuseScore.

So I'm trying to write in an octatonic mode with eight distinct pitches, whose frequency values I provide. The eight pitches are unrelated to pitches in 12-TET. The pitches are defined by ratios to a fundamental/tonic, but I imagine that it would be a lot easier for me to input absolute frequencies than ratios.

Here is functionality I am looking for: (I'm aware that not all of this might be possible)

• Some way to define the pitches that I'm looking for
• The octave (nonave?) is nine units wide on the staff, not eight
• Can I bind "H" to the note above G and below A in this scale?
• Some way to play back the music I write in this mode
• I don't particularly care about accidentals; I don't intend to use them.
• Cool but not strictly necessary: a custom clef

Some options I have considered:

• I saw there is a "Tuning" plugin, but it doesn't seem powerful enough to do what I'm trying to do (or maybe it is, and I just haven't figured it out yet?)
• Maybe I could define a new instrument somehow that can do what I want, similarly to how the drum set staff doesn't mean the same thing as the standard 5-line staff?

I'm using MuseScore 4.0.2, but I could switch back to 3.x if there are plugins written for an earlier version that have this functionality. Thanks so much - I know this is a big ask and not all of it may be possible, but I thought I'd try anyway.

I'm attaching a photo of what a staff with this tuning could look like.