How much headspace exactly? I assume the Pyrex is your secondary based on your explanation, but I'd be surprised if you lost more then a quart from your original 5.5 while racking to secondary. Therefore, there really shouldn't be more then a quart of headspace right?
When I rack to secondary, A) I try very very hard not to get any O2 into the suspension, and B) I VERY carefully move it to a room temp (72ish) space unitl I get some bubbling in the airlock for 24 hours. At that point I assume the o2 has been pushed out of the headspace and replaced w/ c02, and then I carefully move it to the fridge for cold crashing. You generally don't want much headspace in a secondary, but I've done it with up to 2 quarts of headspace before, and being careful with it, it conditioned just fine without oxidation.
Of course, for many of my beers they're gone before subtle O2 effects can yield offtastes, but then again that's a perfectly acceptable way to combat oxidation too (drinking it!).