I'm using Tableau Desktop 10.4 to create some charts and maps for a print publication.
Unfortunately, export quality, whether as png or as pdf (using print to) seems to be quite low.
File sizes are very small (less than 200kb for pdf) which is nice, but I wouldn't mind a much higher file size for increased quality.
Most of the dashboards we build for print are set to 1000 x 800. That seems to be the best for print and imported images are usually created at 300 dpi. I don't know for sure that this will help, but give it a try.