It’s funny you should mention the sarcastic use of “Have a blessed day.” because, when I set myself to researching how long this phrase has been around, I found this definition in the Urban Dictionary from “Mike the Jock”:

Black folks’ code for “Fuck off, Honkey!”

It was Mike’s only contribution to the Urban Dictionary, so it’s rather hard to tell much about him.

Mike was countered by “lovewithpurpose” (her/his only contribution as well):

Someone provided this definition: “Black folks’ code for “Fuck off, Honkey!”
That Cracker really pissed me off, so I told him to “Have a blessed day!” …

and when I saw this I was compelled to provide an alternative definition…. black folk like any other folk are not all the same… In general to tell someone to have a blessed day is saying you hope they experience favor in every area of need… to say this to an enemy can be best define by the scripture Romans 12:20 (look it up)…

Have a blessed day!

I never encountered it dripping with sarcasm, but I can well imagine it said in that oh so saccharine way (some) southern women have of putting people down while maintaining a veneer of manners.