Aside from your conundrum I'm wondering what "ah as in yacht" could even mean; to this puzzled Brit there is no "ah" sound in "yacht". I'd spell it phonetically "yot" - do others pronounce it "yaht" or am I completely misunderstanding?
"Open your mouth and say ah" "tot" "yacht" - these all have very close to the same vowel sound to me as an American, although "tot" is more of an outlier and "taught" might be closer to how I conceptualize of the sound. I'm not sure I'd ever hear the difference in practice.
Sure: “yaht” and “yot” sound virtually the same (at least in American English), only maybe slightly different in the length of the vowel; “folly” and “foley”, on the other hand, sound very different from one another.