We use recent advances on the discretized sum-product problem to obtain new bounds on the Hausdorff dimension of planar $(α,2α)$-Fursterberg sets. This provides a quantitative improvement to the $2α+ε$ bound of Héra-Shmerkin-Yavicoli. In particular, we show that every $1/2$-Furstenberg set has dimension at least $1 + 1/4536$.