I looked around and I do have one nice domestic 6x rate cover.

This is a 12c imperforate #17, together with a pair of 3c Ty I, #25, used to make up the 6 times rate for an overweight letter from Philadelphia to Providence RI.
This was mailed in October 1857, while perforated stamps were coming out en-masse now, but there were still some lingering imperforates.
This cover is neat because of the mixed issue usage, and the fact that the 3c stamps are "not" the more common #26's/Ty III.
I agree that there does appear to be an exponential rarity increase starting around 5x rates both domestic and foreign.