As far as I know, it is not known whether cubical type theories with propositional resizing admit computational interpretations. But here is an obvious attempt: Turn off universe checking locally, and simply define $r : \mathsf{hProp}_i \to \mathsf{hProp}_0$ to be the identity function (or perhaps wrapped in a trivial inductive type, etc). For example in Agda:
{-# NO_UNIVERSE_CHECK #-}
record Resize {i} (p : Type i) (q : isProp p) : Type where
constructor wrap
field
get : p
What could go wrong?