  We study relationships between the restricted unrolled quantum group
$\overline{U}_q^H(\mathfrak{sl}_2)$ at $2r$-th root of unity $q=e^{\pi i/r}, r
\geq 2$, and the singlet vertex operator algebra $\mathcal M(r)$. We use
deformable families of modules to efficiently compute $(1, 1)$-tangle
invariants colored with projective modules of
$\overline{U}_q^H(\mathfrak{sl}_2)$. These relate to the colored Alexander
tangle invariants studied in [ADO, M1]. It follows that the regularized
asymptotic dimensions of characters of $\mathcal M(r)$ coincide with the
corresponding modified traces of open Hopf link invariants. We also discuss
various categorical properties of $\mathcal M(r)$-mod in connection to braided
tensor categories.
