The first AKAs and APAs were converted merchant ships. Eventually the Navy developed, on the basis of Maritime Commission merchant hull designs, classes of AKA and APA that were built for the purpose. The Whitney was one of those - a member of the Andromeda class of AKAs.
A long-defunct plastic kit manufacturer called Renwal used to offer a not-too-bad Andromeda-class ship. Here's a link to one that's currently available on the web - but get ready to recover your breath after you read the price: http://www.oldmodelkits.com/index.php?detail=4655&manu=Renwal
The Revell Randall/Montrose kits represent Haskell-class attack transports (APAs), which looked quite a bit different from AKAs. The APA had a squat, elongated superstructure, containing large berthing, mess, and medical facilities for the embarked regiment of troops. (The standard boat complement of an APA did include two or four LCMs, stowed in chocks on the after well deck, and sometimes on the deck just forward of the superstructure, and APA cargo holds frequently did contain light tanks, bulldozers, and other vehicles - though probably not medium or heavy tanks.) The AKA design had a distinctively-shaped, rather tall superstructure centered well aft of the midships point, a rather sharply-raked bow, and the distinctive A-frame masts. The old Renwal kit has those features. It's obviously not up to modern standards in terms of detail, but with the help of aftermarket parts it undoubtedly could be turned into an extremely impressive model. (I'd be reluctant to pay that much money for it, but I suspect it can be found for a lower price if one is sufficiently patient.)
I built a Revell APA in the markings of my father's ship, the U.S.S. Bollinger, and gave it to him for Christmas. It really made his eyes light up; he kept it on a shelf in his office at Ohio State until he retired. I don't know what happened to it after he died.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.