I play really thick SITs at the moment on the 7 and GHS on my 6, and I shake the fuck out of them. Haven't broken one in forever myself, and I find much better stability in terms of tuning with respect to light strings (after a slightly longer break-in period), but there was the nut problem at first because they were set up with wee little strings. I personally have problems with (1) gripping thin strings too tightly and making them sharp and (2) hitting them way too hard (as in, enough to put a .42 in standard tuning up a whole step or minor third) and making them sharper right on the attack, so I wouldn't know what to say about the strings sharpening themselves other than remembering to tune up to the note and never down and making sure the strings aren't getting squished in the nut because that does happen.
Jeff