Is there a language with non-isomorphic minimum-state UFAs? For all regular languages L, by the Myhill-Nerode classes, all state-minimal DFAs for L are isomorphic. ​ On the other hand, "a regular language may have many non-isomorphic state-minimal nfas". ​ What about Unambiguous Finite Automata? ​ Every DFA is also a UFA, so every regular language has at least one UFA. ​ The natural numbers are well-ordered, so in turn every regular language has at least one state-minimal UFA.

Is there a regular language whose state-minimal Unambiguous Finite Automata are not all isomorphic to each other?
In their paper "A note about minimal non-deterministic automata" Arnold, Dicky and Nivat observe that the problem of finding non-isomorphic minimal automata was solved in a report by Christian Carrez (Lille, 1970).

They give the following example, which happen to be both unambiguous, so are applicable in your case too.