47 - early 49 cabs had a cast base in the middle rear of the cab. Late 49-55 1st series mounted with 2 " shackles " on either side to the frame [the same as your '51 ].
In your case Any late 49 - 53 Chevy or GMC cab will work.
The driver side cowl vent was discontinued with the introduction of the door vent windows in 1951.
You say your truck is a 51 - 51 is the only year with the pull down handles & the vent windows in the doors.
The doors you describe on your truck are for 52-55 1st series, so either your truck is a 52-55 or someone traded out for later doors at one time or another.