I take it escaping means actually escaping, not pre-event avoidance.
Set your smart phone alarm clock with a phone-like alarm sound. Program a time during the dinner party, let it go off, pretend your answering your phone, and then just announce something has come up and you have to go. If people are nibby, look like you're going to cry, to avoid answering their questions about what came up.
The truth is, though, I used to be so good at blending into the background that I could leave whenever and no one would notice I was gone, just as they didn't notice I was actually there. :-)
Sometimes we overthink. Do you really need to do any more than get up and leave, perhaps saying "I have to go now, sorry I can't stay, wonderful meal?"