Exotic Ga-quotients of SL$_2 times mathbb{A}^1$

Every deformed Koras-Russell threefold of the first kind $Y = left{ x^{n}z=y^{m}-t^{r} + xh(x,y,t)right}$ in $mathbb{A}^{4}$ is the algebraic quotient of proper Zariski locally trivial $mathbb{G}_a$-action on $mathrm{SL}_2 times mathbb{A}^1$.