  Using recent results of Battistella, Nabijou, Ranganathan and the author, we
compare candidate mirror algebras associated with certain log Calabi-Yau pairs
constructed by Gross-Siebert using log Gromov-Witten theory and Tseng-You using
orbifold Gromov- Witten theory of root stacks. Although the structure constants
used to defined these mirror algebras do not typically agree, we show that any
given structure constant involved in the construction the algebra of Gross and
Siebert can be computed in terms of structure constants of the algebra of Tseng
and You after a sequence of log blowups. Using this relation, we provide
another proof of associativity of the log mirror algebra, and a proof of the
weak Frobenius Structure Theorem in full generality. Along the way, we
introduce a class of twisted punctured Gromov-Witten invariants of generalized
root stacks induced by log \'etale modifications, and use this to study the
behavior of log Gromov-Witten invariants under ramified base change.
