No, I did not. I do not have a computer set aside with iTunes so I just dropped in to an Apple Centre where one of the techies I approached suggested that it could be a hardware issue that was made apparent by the iOS update from 5.1 to 5.1.1 before telling me that they worked through an appointments system. I promptly made an appointment for the Genius Bar online for them to sort it out as the iPad was still under warranty not to mention the Apple Care.
As you'd expected of a slightly intermittent error, the sleep/wake button promptly began to behave itself as soon as I handed it to the techie at the appointment. He was kind enough to still take it out the back to perform a few tests, one of which may have been a restore. I did suggest he power cycle it as it was the only other thing which involved the button. He told me later that when he did, it chucked the iPad into a perpetual on/off cycle which they identified to be an irreparable hardware problem - at least in so far as the abilities available to the store. They then gave me a replacement, which is a factory refurbished piece, one with repaired/double-checked innards and a new case/outside.
Took a while to get it back up to speed as I had disabled iCloud backup back when I was thinking that I didn't need it, not to mention it'd chew into my monthly quota while I wasn't looking. The upside, though, is it let me leave apps out of the reinstall I forgot about installing when I was learning the iPad. In any case, decided to fiddle with the settings this time around so It'd do what I wanted.