I finally found something about talking with your mouth full, but it's out of period. It was in Maureen Waller's wonderful book: 1700 Scenes from London Life. In it she quotes from Hannah Woolley's 1675 etiquette book: The Gentlewoman's Companion as follows:

Above all, The Gentlewoman's Companion urged its readers not to "fill your mouth so full, that your cheeks shall swell like a pair of Scotch bagpipes" and to "close your lips when you eat; talk not when you have meat in your mouth; and do not smack like a pig, nor make any other noise which shall prove ungrateful to the company."

Now I would assume that English diners would have become even more fastidious in their habits in the ensuing century after Woolley's book was published, but of course I can't say for sure. I shall keep searching for something contemporary with Austen.