Recently another swedish genealogist forwarded your request to me.
My Ek ancestors were also from Varmland (N.Bogerud Parish). From your brief outline I am relatively sure we are not related. The Ek name in my family also was generated by the military but back somewhere about 1765. They used the Ek name after that point rather than the patronymick.
My parents came to the US in 1923 so we are newcomers. I lived in Michigan for many years but my parents stayed in NY.
Have you tried any of your queries on the Swedish genealogic Sites such as Anbytarforum? I have gotten much useful info from them.