Ya dark leafy greens and ginger don’t mix well with coumadin. 
I don’t know how reliable this site is, but I found guidelines on it for dark greens and regular greens for people who take coumadin: http://www.healthatoz.com/healthatoz/Atoz/common/standard/transform.jsp?requestURI=/healthatoz/Atoz/dc/cen/hea/meds/coumadin.jsp
Here is another site that is aimed at people who use coumadin. Again, not sure how reliable it is, just what I found on a quick look-see: http://www.drgourmet.com/warfarin/vegetables.shtml
You should ask your doctor about those, if it’s good information, and let me know what he says if you can…I run the Rawbetes community and many of them are on various medications and run into the same types of issues. And I’m not a healthcare professional or nutritionist, so I have no idea lol.
Some people do more fruit on raw diets - but with the diabetes…ya. Poor you, your between a rock and hard place!. Although I’ve run into some people here and on other sites that have diabetes and supposedly fruit doesn’t effect them so much. Not me though, they still hit me hard. Maybe when I lose more weight I can have more.
Although you can’t do dark leafy greens, other fruits and vegetables lower in vitamin K will still give you benefits and lots of nutrients. Good luck with the big push!! I’m sending you lots of good wishes and vibes.