Ordered new gasket; was surprised when "standard shipping" resulted in the part arriving the next day. Installation took all of five minutes, although a good ten were needed with a heat gun in order to get the gasket to return to its original shape after having been boxed.
Only downside is that I didn't notice that the gasket on the freezer door is toast as well, until I'd removed the refrigerator door. APP shows it in stock, so I'm hoping to have that repair out of the way shortly.