[tavianator]

You may want to look into improvements to A* for grids, like Rectangular Symmetry Reduction.

[taneq]

Also jump point search: https://zerowidth.com/2013/a-visual-explanation-of-jump-poin...

[dietr1ch]

If just use A*, but you rank open to loop for lowest (f, h) pairs, then the search frontier just dives despite having multiple optimal paths, as the new node tie-breaking ensures we prefer nodes that seem closest to the goal.

[porphyra]

afaik jump point search would work for uniform cost grids but not if there's the exponential term that OP has