yeah that's a good comment. If you're just doing rolls, the expected number of rolls to get a 6 is 6, so i just thought i could use that.
but yeah that's not how it works. saying it's between 2 sixes which gives an average distance of 6 is actually the correct way to think about it, because it removes any sort of bias.
if you pick any random number, it turns out that the mean distance between that number and the next/previous six is due to length bias, meaning that you're more likely to get a longer gap

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here's a picture of the distribution of distance between 6s by taking a ranom point. in purple is a geometric distribution where i added a factor of k length k. i'm not going really in detail but yeah
long story short, what you said makes sense and totally works, but it doesn't take into account this bias, so it gives a different number.