Almost excellent unique factorization domains

Let ( T , 𝔪 ) be a complete local (Noetherian) domain such that depth T > 1 . In addition, suppose T contains the rationals, | T | = | T ∕ 𝔪 | , and the set of all principal height-1 prime ideals of T has the same cardinality as T . We construct a universally catenary local unique factorization domain A such that the completion of A is T and such that there exist uncountably many height-1 prime ideals 𝔮 of A such that ( T ∕ ( 𝔮 ∩ A ) T ) 𝔮 is a field. Furthermore, in the case where T is a normal domain, we can make A “close” to excellent in the following sense: the formal fiber at every prime ideal of A of height not equal to 1 is geometrically regular, and uncountably many height-1 prime ideals of A have geometrically regular formal fibers.