Are there accepted halachic opinions that say Birkas haMazon can be said after a full meal excluding bread?
I am not aware of such an opinion and find it highly unlikely. In Igros Moshe O.C. 4 :41 Rav Moshe Feinstein writes that it is not possible to say Birkas haMazon without eating at least a Kezayis of bread. If the meal includes cake or crackers of an amount similar to the quantity of bread one would normally eat then there is Kevias Seuda and Birkas Hamazon is
required (see end of Teshuva).
Ilan Segal