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Sorry to belabor this, but if bullet stability is not a function of BC, what is it a function of?
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No stability is not a function of BC, BC is a function of the bullets shape. Long skinny pointed bullets will have a higher BC than short blunt fat ones, to put it (ultra) simply.
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Is there some minimum muzzle velocity for any given bullet and barrel length/twist? Are we "doomed" to learn about each bullet's stability with each gun by trial and error; hopefully not...
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Yes, but generally not by YOUR trial and error. Most of the work has been done for you, its in your loading manual, if you dont see a bullet weight listed, thats because its not right for the "normal" twist fort he caliber, BUT, you have to keep in mind that, #1 copper bullets introduce a new variable (long for weight). and, #2, The whole twist rate/stability thing is, to quote capt. barbossa, "more what you'd call "guidelines" than actual rules"........ That is, not ALL .257 WBY rifles with a 1in10 twist will shoot that bullet poorly. As anyone who is into guns eventually finds out, each gun is an individual as far as what it shoots good and what it shoots poorly. Its possible the next rifle off the assembly line after yours shoots 115gr barns TSX into super tight groups. (its also possible it shoots them just as poorly)
For the most part, you wont go wrong following conventional wisdom as far as bullet weight/twist, but there are always exceptions, (monolithic hunting bullets being one of them). Some rifles with "to slow" twist rates will stabilize "to heavy" (long) bullets, while some rifles with "correct" twist rates wont stabilize "correct for twist" bullets..... And even when the twist and bullet length are perfectly matched, sometimes your gun just plane wont like a bullet/powder/primer/brass combo.... we just have to keep plugging along till we find one our gun likes...