Yes, agree: a better way of combining “refine” with “gridinterplayer” would potentially speed up the computation of the steady state.
I tried to suggest an improvement for “gridinterplayer” in this post, but it does not consider any d variable. Still, maybe the idea is useful: Faster Aiyagari example with interpolation
The performance of the transition is another issue, though. There we do the value function by backward induction over time, like in a life-cycle model, and we don’t use refinement (please correct me if I am wrong). Hence refinement if not responsible for the slow performance of the transition in infinite horizon models.