Denny,
Thank you very much for your careful research and explanation.
Another reason the cross braces might have been removed and sometimes replaced (later) is that a quick "fix" to upgrading an older truck to a high-pressure 235/261 engine was to mount the radiator in interesting ways on the core-support. This was "necessary" because the late-55-to-63 water pumps most likely had long shafts that would have hit the radiator.
Eileen,
You might have jumped to a few incorrect conclusions in your second paragraph. Not enough of the core support is viewable (perhaps) in the Factory Assembly Manual and Brownell's book to be able to see the differences in 47-55 1/2 ton Advance-Design radiators supports/frames (and to be able to say that Woody's is the same - but, his might indeed look like them).
If you are referring to both of them showing the cross braces, you are correct.
Denny's information about 1947-55 regarding cross braces is interesting: however (as stated by Denny) 47-48 are different from 49-53 (1 base-bolt vs 2 base-bolts), and both are different from 54/55 (which have captive nuts for dual horns mounted on the front of the core support, and two base bolts).
The 1947-55 Factory Assembly Manual shows parts for 54/55-1st series for most of the parts.
Tim