Stratified Random Sampling with large dataset in ArcGIS?

I want to create a Stratified Random Sample with a land cover classification map. The purpose for the Stratrified Random Sample is to produce an Accuracy Assessment. I am using ArcGIS 10.2 with access to Spatial Analyst and all other tools.

I have six land cover types and I want 300 random points for three of the classes I am interested in.My first step was converting my raster to polygon. The result gives me over 3 million polygons to work with.

I have tried the Dissolve tool and making multi-part polygons, but some of my classes are too large, which results in an error message "Topology Invalid (Out of Memory).

I have tried using the Merge in the Editor toolbar. Again, due to my large number of polygons in some of my classes, it freezes and crashes ArcMap.

I would like to do the stratified random sample on a raster, rather than converting it to polygon form. Is this possible?

Are there any other tools/programs that I should use that may help combat my large dataset issue? I have consistently run into problems because I simply have too many polygons per land cover type.