  In 2003, Rodriguez Villegas conjectured 14 supercongruences between
hypergeometric functions arising as periods of certain families of rigid
Calabi-Yau threefolds and the Fourier coefficients of weight 4 modular forms.
Uniform proofs of these supercongruences were given in 2019 by Long, Tu, Yui,
and Zudilin. Using p-adic techniques of Dwork, they reduce the original
supercongruences to related congruences which involve only the hypergeometric
series. We generalize their techniques to consider six further supercongruences
recently conjectured by Long. In particular we prove an analogous version of
Long, Tu, Yui, and Zudilin's reduced congruences for each of these six cases.
We also conjecture a generalization of Dwork's work which has been observed
computationally and which would, together with a proof of modularity for Galois
representations associated to our hypergeometric data, yield a full proof of
Long's conjectures.
