As said above, a 65 Barracuda VIN beginning 185 is for a slant six car. VIN for a 65 Barracuda V8 would begin V85. (8 means Barracuda or taxi, 5 is the year, next digit would be the assembly plant; 7 would indicate St. Louis.)
I've never seen a VIN tag with two of its numbers stamped in with what looks like a punch, from the front, with the rest of the numbers stamped in from the rear. Doesn't mean it never happened; I wouldn't know. But the VIN tag being riveted on sure is a red flag for it having at least been removed and re-installed. And if your car shows no signs of ever having been slant six powered, I'd sure be thinking that maybe the VIN tag was switched.
Don't know what to tell you. A 273 2-barrel 65 Barracuda isn't real valuable, and I wouldn't worry about not having an original fender tag, but that funky VIN tag is another matter. You say the State of Missouri gave you a title without ever actually looking at the car? I can tell you that in Florida a law enforcement officer would definitely look at the car before you could be issued a Florida title. Whether that officer would accept a riveted VIN tag with strangely stamped numbers, I don't know. But if I were a potential purchaser, it would give me pause.
