You are correct, the codes on the heads are date codes, June 5 of 69 and May 29 of '69. I do not know the end of production for '69 model year, but your August build date is either very early '69 or very late '69. If you have a PHS, what does the billing history say for order date and delivery date?

YE is a 350 2bbl in 1969. There will be another number down along the timing cover behind the lower radiator hose that will contain the last six digits of your VIN if the engine is numbers-matching.