"Based on the turbotax guidance and prompts it is 6, because I had both non-HDHP and HDHP in the same month. "
I don't think that this is what it meant (wherever you saw this).
What matters is "What coverage did you have on the first day of the month?" That determines your coverage for the whole month (even if it changes during the month). By this metric, you had HDHP coverage for 7 months.
I believe that the sentence you refer to meant "if you had HDHP and other conflicting coverage in the same month", then, normally this would mean that the HDHP no longer counted.
However, since you have clarified that your non-HDHP coverage started AFTER the first of July, as far as the IRS is concerned, you had HDHP coverage for July with no conflicting coverage.
Make sense?
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