Pete,
The problem with making a mid or late war Grayson from the Buchanan "45" kit has several problems. None of the first 24 Benson-Gleaves were authorized to have and hence were not modified with the raised centerline platform for a 20-mm gun or had bridge wing 20-mm guns installed. The authorized 20-mm armament for this group of ships was only four mounts. So the navigation bridge isn't right for the Grayson. Further, the Buchanan "45" kit doesn't have the deckhouse for the second aft TT mount and that would take extra work over just using the new Livermore kit as a starting point. Also, the Grayson had a half shield canvas covered 53 mount. See the first two images, when Grayson was updated to the two twin 40-mm configuration at Pearl Harbor in June 1943, she had the "open" 53 mount enclosed again. A kit-bashing between the Livermore kit and Buchanan "45" kit may be doable or just hand-making the twin 40-mm tubs for the Livermore kit may be easier. But, the Buchanan "45" kit was a limited edition release and may be difficult to get at some point.
In 1945 Grayson was one of the Gleaves class units to receive the anti-kamikaze mod (two quad and two twin 40-mm mounts and two twin 20-mm ... before the bridge ... and two single 20-mm ... on the main deck). At this point anyway, NONE of the Benson-Gleaves kits will build the anti-kamikaze version out of the box (see the third image). Many of the configurations seen with this class will require modification to the basic kit to build an accurate model.
So after all that, I agree with Dick that the Livermore would be a better start for building a Grayson for either the early Pacific war period or during the mid-war period up to about May 1945.