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Your detailed account speaks volumes; thank you !
I'm likely to get flamed for saying this, but let me begin by describing your issue with 3 little words :
Not.Enough.Tension. [only ~122 pounds, as per published figures in the GHS database PDF]
Some players would not notice what you explained, but MY 66 year old ears still would.
In comparison, the long scale GHS Precision Flats [which you praised] are said to be 163 pounds or higher tension when tuned to pitch on a long scale bass.
I'll bet a dollar to a doughnut that short scale GHS Brite Flats would be fine on those two basses of yours [~150 pounds tension].
Their short scale Balanced Nickels are somewhere in between the two other GHS types in tension, BTW, [~143 pounds tension], so prob'ly high enough.
I am curious about something else.
How many of your other approximately 38 basses are short scale ?
Are any of them medium scale ?
If any of them are short or medium, what is your experience stringing those ones ?
BTW, I would completely expect the RotoSound short scale RS 66 sets to have the same issue, and for the same reason.
If your trash has not yet been picked up, try those strings again on one of those basses, and deliberately tune them 2 or 3 semitones above standard pitch, then check the intonation, tuning, and feel.
Let us know how stable they become.
I'm pretty sure that I know the answer.

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