Which toolbox in ArcGIS do you use to analyse the Landscape metrics? Fragstats?As I know, the circuitscape and linkagemapper could be available to solve this kind of problem about the landscape for fragmentation,which can be compatible in ESRI ArcGIS as a toolbox, but also independent as a GUI.BTW the path analyst is used for the optimal Least Cost Path analysis,which be not suitable for your research.Hope useful for u.

Dear Connor,

If ArcGIS crashes, maybe it is time to switch to R...

In R, you can use packages 'raster' and 'landscapemetrics' for loading raster data and calculating Fragstats and other landscape metrics.

HTH,

Ákos

it seems you have, in part, answered your own question. If you know how to handle the task in a vector map why not transfer the raster map to a vector? This can be done in ArcGIS or in R. Euclidian distance is, indeed, straight line but if you're working with area patches, hexagons, etc. remember that this would be from the centroid of an area and thus have some ambiguity. If you are using cities or towns in a patch or area to those elsewhere, there are more precise tools in the toolbox--again, R or ArcGIS--than the measuring ruler.

I'll also note, in passing that my preference remains the ArcGIS environment. I respect QGIS as a good, free program. And I like it. As to R, there is a learning curve here--as there is with the other two programs mentioned here. For me it's fairly steep. So my general advice would be work in the program you know for this project while exploring other potential tools for later work.