"I have a quick release on the front wheel only, alas."

How exceedingly strange! The only reason not to have quick-release wheels that I know of is paranoia about having the wheel stolen. Why would somebody worry about having the back wheel stolen, but not the front?

If the bike is still at the bike shop, ask them if they can put a quick-release lever on the back wheel for you. Really, getting the wheel off is the hard part of fixing a flat.