  We exhibit a smooth compactification of the moduli space of elliptic curves
in a product of projective spaces with tangency along a subset of its toric
boundary divisors. This is a Vakil--Zinger type of desingularization for maps
to a product of projective spaces using ideas of elliptic singularities and
logarithmic geometry, extending the recent work by
Ranganathan--Santos-Parker--Wise. We use this to construct the virtual
fundamental classes of the spaces of genus 1 maps to a special class of simple
normal crossings pairs.
