Has anyone seen a NP graph problem like this before?
This is known as the distance-$d$ independent set, i.e., you are looking for an independent set of size $k$ where the distance between every two elements in the solution is at least $d$. 

The problem is NP-complete even on planar graphs according to [1], but I don't know about its complexity on partial grids.

Regarding reductions, you can probably take the $d$'th power of the graph and find a (distance-1) independent set in that. The claim is that any solution here is a distance-$d$ independent set in the original, but you need to verify this.



[1] Eto, Hiroshi, Fengrui Guo, and Eiji Miyano. "Distance-$d$ independent set problems for bipartite and chordal graphs." Journal of Combinatorial Optimization 27, no. 1 (2014): 88-99.