Okay the answer. But first - thanks to all for not picking up on the spelling of Hays' Brigade!
And the winners of the $1000 prize. According to a report from a May 1864 Confederate monthly magazine - the winners, after a two and half hour contest were the men of Hays 'Ironclad' Brigade. Still to find the end time scores. A task for someone with access to Confederate newspapers from this time.
Thanks Steve for the info on Alexandria - so, maybe, Baseball should be looked at one of influences on Grand Strategy - did Chattanooga or Atlanta have any good fields?
Would be interested to hear of any other reb baseball games.