Exhaust Manifold Casting Numbers

How could I have manifold #3614368 for a '69-'70 340 dart dated 2.29.72?

Because it's not a 69-70 manifold. IIRC the correct last three digits for a 70 exh are 549 and 553

That number is 72-73 A body 340 IIRC. The reference you used is wrong, likely mymopar.com is my guess.

If your car is a Duster 340 and it was built after the casting dates, then yes, they would be the correct exhaust manifolds