I can see only one piece of text you haven't considered. In between the two excerpts you've noted comes:
"Together we score one hundred and forty-four. Your numbers were chosen to fit this remarkable total: One Gross, if I may use the expression." No cheers. This was ridiculous. Many of his guests, and especially the Sackville-Bagginses, were insulted, feeling sure they had only been asked to fill up the required number, like goods in a package.
That seems to indicate that there were one hundred forty-four guests altogether, though of course how that includes Frodo and Gandalf, who would not have been among the "one hundred and forty-four flabbergasted hobbits", is at best unclear. Or, one could guess that there were one hundred forty-four guests invited (plus Frodo and Gandalf), and that the one hundred forty-four flabbergasted hobbits included only those who had been invited, and not Frodo.
It may be worth noting that the "hundred and forty-four guests" idea goes back to what Christopher Tolkien describes, in The Return of the Shadow (part of "The History of Middle-earth"), as "The Second Version": the first revision of Chapter 1 of The Lord of the Rings. This version says:
To that party invitations had been limited to twelve dozen, or one gross (in addition to Gandalf and the host), made up of all the chief hobbits, and their elder children, to whom Bilbo was related or with whom he was connected, or by whom he had been well treated at any time, or for whom he felt some special affection. ... All the 144 special guests expected a pleasant feast. ... Not one of the 144 were disappointed: they had a very pleasant feast. ... One hundred and forty-four flabbergasted hobbits sat back speechless.
Here it appears that there were one hundred forty-four hobbits invited, not counting Frodo, Gandalf, or any other non-hobbits.