May 27 64 date is from Henderson. I use the source all the time, but we all know its precision is nowhere near 100%. Rules and Bylaws of the Columbus Guards, 1883, list W S Davis as killed at Spotsylvania, no date given.

If we go to May 27 64, Benning's brigade finished 6-7 miles east of Ashland, taking up a portion of the Totopotomoy line next day. In moves of 1-3 miles a day, they slid east, behind friendly lines, to their position at Cold Harbor, at Johnson's Farm, arriving there 1 June. Particularly sharp skirmishing, with loss, was reported May 30 and June 1, and there was fighting and skirmish work there until 10 June.

The primary sources I have show the men considered the campaign a continuum, rather than a discrete series of events. If there's no additional context, you need to allow some latitude when places like "Spotsylvania" and "Cold Harbor" are named.

The newspaper article - is there more than you transcribed, or any more context as to when exactly it was written? If a letter wentby mail and was recieved June 11, it could have been written anytime in the preceding 3 to 30 days.