Your is a common problem with Word and I have the impression that Microsoft didn't like so much the idea to enhance the compatibility with Openoffice. I would like to suggest the use of Latex, BTW it is not always possible.
Since you noticed that you can produce the desired effect exporting as PDF, I decide to report here an interesting blog page for MacOS that can used to get hints to import a vectorial PDF inside Microsoft Word: the procedure is not fast but it avoids to fix the draw on a grid (as you do converting to PNG).
The main solution is based on
Once that you have your PDF (or eps) file you can convert in EMF by command line too.
Those are some command lines suggested:
pstoedit -f emf diagram.pdf/eps output.emf
pstoedit -f emf -pta diagram.pdf/eps output.emf
Place letters individually, if text looks odd
pstoedit -f "emf:-m" diagram.pdf/eps output.emf
Use Arial as font, if font looks wrong
pstoedit -f emf -drawbb diagram.pdf/eps output.emf
Force drawing of bounding box – try this if you get cropping
pstoedit -f emf -xscale 2 -yscale 2 diagram.pdf/eps output.emf
Scale up – use this if lines look blocky; experiment with larger values than 2
pstoedit -f "emf:-m" -pta -drawbb diagram.pdf/eps output.emf
A combination of some of above
You can search a program to manage images that works fine with vectorial format under your operative system. Maybe you want to give a look to inkscape or intaglio for OS.
At the end you may prefer to fix the grid if the image as PNG file, maybe with the same resolution of the printer you're going to use (even 600 dpi or more if this is the case) and to save your time.