Hi,
The low 300,000 serial number range on my "flat latch" + "diamond stock" original Model 36 dates it to around 1964. Indeed, you have one of the last of the flat latch models.
When I see a flat latch and/or diamond stocked Smith in a gun shop my knees get a little weak . . . and sometimes my wallet gets a little lighter too!!!
Here's mine in a Mitch Rosen UPL left-handed holster . . . a great holster for a classic revolver indeed!