There is a NC State Census record for a Walter ASHMORE, of Surrey, NC, which bears some similarity to the household composition of Walter ASHMORE (d bef 11 Jan 1791 - York, SC):
Walter ASHMORE: 1 - 4 -- 4 -- 0 - 0 -- 9 [Surrey, NC, 1784-7]
The first figure ("1") reflects males age 21 through 60. The second figure ("4") reflects males under age 21 & above 60. The third figure ("4") reflects all white females. The fourth figure ("0") is for blacks age 12 to 50. The fifth figure is for blacks under 12 & over 50. The final figure is the total number of persons in the household.
Walter ASHMORE is presumably the male age 21 to 60. Sons William and Walter would seem to be included in the second count of four (4). There would seem to be some combination of two other boys under age 21 or men over 60. The female count would seem to include a wife and daughters: Margaret, Mary and Ellinor.
Absent some other linking record, it is far from certain that this is the SAME Walter ASHMORE later found in York, SC. However, to the extent that this IS the same Walter ASHMORE, the record would seem to suggest that ALL of Walter ASHMORE's children were already born by the 1784-7 date of the State Census survey. There might be some additional data on the original underlying Census records showing more precisely WHEN the canvass of Surrey, NC, took place.
This record also presents the bare possibility that the John ASHMORE later found in Greenville might have been another son of Walter ASHMORE OMITTED from mention in the Will, perhaps because Walter believed that he had been adequately provided for during his lifetime.