Products of Michael spaces and completely metrizable spaces

For disjoint subsets $A,C$ of $[0,1]$ the Michael space $M(A,C)=A\cup C$ has the topology obtained by isolating the points in $C$ and letting the points in $A$ retain the neighborhoods inherited from $[0,1]$. We study normality of the product of Michael spaces with complete metric spaces. There is a ZFC example of a Lindelöf Michael space $M(A,C)$, of minimal weight $\aleph_1$, with $M(A,C)\times B(\aleph_0)$ Lindelöf but with $M(A,C)\times B(\aleph_1)$ not normal. ( $B(\aleph_\alpha)$ denotes the countable product of a discrete space of cardinality $\aleph_\alpha$.) If $M(A)$ denotes $M(A,[0,1]\smallsetminus A)$, the normality of $M(A)\times B(\aleph_0)$ implies the normality of $M(A)\times S$ for any complete metric space $S$ (of arbitrary weight). However, the statement `` $M(A,C)\times B(\aleph_1)$ normal implies $M(A,C)\times B(\aleph_2)$ normal'' is axiom sensitive.