Message from my Rosh Yeshiva Rav Avishai David:
When Rosh Hashana falls out on Shabbos there is an obligation of Seudah Shlishis. There are several approaches to deal with this issue. The one I recommend is the following.
Divide the main Yom Tov meal on Rosh Hashana day into two parts.
After eating the first part of the meal, say Bircas Hamazon (Bentsch) and then wash again for the third meal(Seudah Shelishis).
Wait approximately a half hour or so between the meals or go for an enjoyable Yom Tov Tiyul outside with your family.
Wishing everyone a Wonderful Yom Tov and a כתיבה וחתימה טובה