In Map Algebra -> Raster Calculator, you can use an expression like:
Con("landcover"==5,1)
Translation: for every pixel in the land cover raster, if land cover value is 5 (or whatever your forest gridcode is), make the output value 1 (or whatever value you want), otherwise make the value NoData. Now when you convert to polygon, it will only consider 1 vs NoData, so many less separate conversions.