A1c is definitely driven by highs and lows. which definitely drive average BG, which defines A1c, and round and round we can go. That's not the question or the issue here.
The OP is asking, specifically, about the ratios of highs to lows and how those relate to his A1c. The reason why SD is such a horrible parameter to use to answer this question is, specifically, because it ialready assumes within that calcuation itself that his ratio of highs to lows is exactly 1, even if it isn't.
You must understand that even if your actual BG data are skewed as hell to either highs or lows, if you calculate a standard deviation for your data, the calculation itself will simply treat the numbers as if they are not skewed to either the high or low end.
Without your average reported, you can't even report your SD and have it mean anything at all.
So, let's say your average is 86. Then, what your SD says is that you can expect about 68% of all your other actual readings to lie between 106 and 66, and about 95% of your actual readings lie between 126 and 46. That's it. That's the meaning, period, even if your data don't actually do that.
You can do a frequency distribution for every single BG reading you've already taken and determine where your variation actually is based on real numbers rather than a calculation from a formula that may or may not represent what your data actually look like.
Yeah, it's extra work, but that's the exact question that the OP is asking and there is no shortcut to the answer.
I'll add that the OP used the parameter "time", as well, which is way beyond the scope of the SD, unless you are actually measuring time itself, which we obviously are not.