your math on the drain actually checks out, nick. if you drained a third and refilled, you'd expect roughly a 33% reduction - so if you ended up at 110, you were probably sitting around 160-165 going into fall. that's not uncommon if you were using trichlor tabs all season, since each pound of tabs adds about 6 ppm of cya on top of the chlorine. it stacks up faster than most people expect.
for where you are now, i'd plan on draining closer to 40-45% before you bother shocking. at 110 ppm your free chlorine demand goes way up, and you'd need to hold fc somewhere around 15-20 ppm to get meaningful sanitizing against algae. that's expensive and hard to sustain. once you dilute down to the 40-50 ppm range you'll be in a much more manageable spot. if your fill water is cold like nroberts mentioned, drain slowly, refill slowly, and keep an eye on your heater settings so you're not stressing the shell or equipment with a big temp swing. test again before you add anything, because fill water chemistry can throw off your baseline more than you'd think.