Well, *that* was interesting!
Firstly, as a few have mentioned here, the 6th-generation classics are more tightly-sealed than their immediate forebears, so the otherwise-useful plastic tools included in the battery-replacement kit won't cut it all by themselves; artful (and careful!) application of the metal spudger tool was also required. Thankfully, years of freelance IT work on recalcitrant Macs of all stripes helped prepare me for this bit of improvisation, even though this was the first time I've taken a crack at an iPod (my own 120GB classic - thin version). Happily, other than twisting that one metal clip near the headphone jack - apparently impossible to avoid - and some very minor cosmetic damage, the balance of work went without a hitch. I speculate why Apple makes us go though this, but that's for another thread. Thanks for the kit and tools!