This is an interesting linguistic phenomenon, and I'd be interested in someone with more linguistic expertise analyzing it. One of the distinguishing features of sophisticated language is its recursive properties; the rules of grammar can take basic linguistic units such as nouns and verbs and use them to form phrases that can themselves be used as linguistic units to form more complicated phrases.
In this case, though, recursion fails: the sequence of words "only dinner in Texas for us", is a noun phrase, and one can fulfill many of the functions of nouns. It can, for instance, be a subject complement: "This was the only dinner in Texas for us". But its use in this particular case to take the place of a noun fails.
I think that where the sentence you present runs into trouble is that the phrase is a restrictive phrase; that is, it defines a particular instance. This then demands a definite article. The indefinite article "a" doesn't go well with the word "only". The structure suggests a general category of "only dinner in Texas", and indeed different people can have different only dinners, so there is some sense in which there are multiple only dinners. Moreover, there are multiple dinners that could have been the particular speaker's only dinner, so there is a coherent meaning even with the "for us" qualifier. However, the contrast between the nonrestrictive "a fitting" and restrictive "only" remains quite strong. The sentence would be much clearer with hyphens more clearly grouping words into compound ideas: "It was a fitting only-dinner-in-Texas-for-us." Or if it were reworded, such as "It was fitting that that was our only dinner in Texas".