Originally I got the exact same thing.. same oil, same filter, same interval.. Noise the second start after an oil change. Dumped that oil and replaced with the same, did it maybe once more.. then hasn't since.
I am convinced this is a design issue with the chain tensioners where depending on how the cams come to rest backward pressure can be applied and the tension on the chain compresses the tensioner, so slack is left on the other side until you go to start the vehicle. Then the tensioner needs oil pressure before it can pump up and effectively take up the slack to prevent slapping. There is a small ratchet assembly on the tensioner that should prevent this but I've seen pictures of the pawls flattened out.
The crank/cams not always coming to rest in the same spot means the valve springs could be pushing them clockwise or counter clockwise, to explain why some cold starts do it and some don't.
In reality I think the tensioners are a bit more complex, with some kind of check valve in there to control oil flow out of the assembly, and I think for some reason different oils or maybe deposits in this area are keeping the little ball and spring from working correctly. This is the only reason I can come up with that oil would impact the operation.
OR.. a start up with no oil in the system (like after an oil change) does something to the tensioner so subsequent shut downs compress the tensioner.. but it eventually sorts itself out for some reason I don't understand.
If it keeps up I'd consider dumping the oil and switching to a thicker formula. With your mileage and gulf coast ambient temps that may not be a bad idea anyway.