Having an impossible time decoding

In your original post you wrote "... I'm also curious if there is a concrete way of telling which transmission belongs in the car, without the build sheet that is....".
As toolmanmike said it is a 273-2/4 speed car. There a few codes on the fender tag that document this. First for the Dart engine in 64 the 1st digit of the VIN is 7 for Dart 6 cyl and L for Dart 8 cyl. The 2nd digit in the vin of 3 maps to Dart 270, the 3rd digit of 4 is for 64 model year, and the 4th digit of 5 means it was built in the LA plant. Then the fender tag codes map to sales codes based on the LA plant mapping (for 64 each plant used it's own fender tag mapping to sales codes). Any number below the C would be the engine code which would only be used if there was a different engine then the standard. You don't have anything there which makes sense as you have a 273-2 (1st digit of vin) and I believe the 273-4 charger motor was not available until the 65 model year anyway. The 3 below the A maps to sales code 343 which has a description of "Transmission-4 speed A833 manual floor shift". And for 64 Dodge A bodies the body code of L33 on your tag maps to "Dart 270 4 door sedan 273-2". So that should answer the engine/tranny question you had.
Your trim code of H1Q, H is high bench seat, 1 is cloth and vinyl, and Q is turquoise.
Your paint code of JJ1, J is Aqua the first one for roof the second one for body, and the 1 just means mono-tone (body painted in one color vs two-tone).
The 1 below the H maps to sales code 361 which is radio-am music master/economy.
You then have a P of K and an R of 7. This is where the galen book does not help as for LA plant 64 it only lists mapping for the digits below A, C, H, and L. And for all the other plants it does not show a mapping for the P and R.
Anyway, hope this helps. It's nice to see a survivor in such good condition. Those of us living in the rust belt are envious of those that don't and can come across jewels of 55 year old cars with very little to no rust. Extremely rare to come by in this climate. Hope you enjoy her.