Thanks guys. I continue to research the rifles mentioned and more. Some very interesting history.
The search for a rifle chambered in the 6.5 is about inherent accuracy. 'Course you need a good barrel to take advantage of the bullet. I am not looking to reload for 1000 yards nor will I hunt with the rifle. The rifle will be used for competition and will not be reloaded hot.
Observation: Reading over the posts and reading another thread on Rifle Country, it seems that trends develop about certain rifles. The Enfield seems to be the "cycling" king with "satisfactory combat accuarcy". Perceived recoil of the Mosin Nagant is very subjective. Seems as if cost is the deciding factor in a lot of cases.
The accuracy winner seems to be the K31. While I am still leaning toward a 6.5x55, the K31 may have influence. As much as I like the 03, I do not want a 30-06. The K31, which, apparently, duplicates a 308 could be handloaded to fit my liking without sacrificing accuracy.
The Swedish Mauser 96 is also in the running.
"The m/96 is a very accurate service rifle. This was proven during the early years of the 20th Century, when the various powers held international service rifle matches. The host country provided the rifles and ammunition used in these matches to all of the teams so that all competitors used the host nations service rifle. In the entire history of this series of matches, the best scores across the board were not shot with the U.S. M-1903 Springfield, the British Lee-Enfield, or the vaunted German Model 98 Mauser, but with the Swedish m/96 and the Swiss Schmidt-Rubin rifles. These are the most accurate of the classic bolt action military rifles. No collection of military Mausers should be without a Swedish Model 1896."
http://www.chuckhawks.com/swedish_mauser.htm