Complex Shapefile Compression Advice

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I'm looking for some advice on how I can simplify this very detailed shapefile to ultimately be used for the web (as topojson) as a interactive heatmap. It was originally created from a raster file (geotiff - http://ecotope.org/anthromes/v2/data/). I believe it's going to take a little more massaging before using a Douglas-Peucker or Visvalingam algorithm. I believe the best way to achieve this would be to intelligently merge features based on the attribute value each contains. I'm just not sure the best way to achieve this. I have a sneaking suspicion that "dissolve" is what I need, but QGIS just freezes anytime I try that.

I'm working with command-line gdal utils and QGIS.

I have attached some screenshots below to give you a better idea of what I'm dealing with. Any advice would be very much appreciated! Thank you.









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