Now regarding the 350-scale Veteran Models' accessories, I concur with everything you say about them - however rather than going with such larger parts as these, I would strongly recommend upgrading instead with 1:600-scale - that is, undersized - parts.
This is, first of all, in accord with a "Basic Principle" of getting away with scale mismatches which will still end up looking "close enough": if you have to err, be sure to do it on the side of being UNDERSIZED. And the Second Rule of Thumb (in "my book", anyway) is that you can usually always get away with about 15% scale-mismatch. Now it's true that, for your 500-scale King, 1:600 scale accessories will be fully 20% undersized - still, your 350-scale Veterans' parts are a whopping 43% OVERSIZED!
These two "deal-breakers" - oversized and by +43% - combine to be particularly apparent forward, where the ASROC is so much larger than the 5-inch Turret. And of course also at the stern where both the CIWS and Missile Launcher (which you did not mention but I will confidently predict is also [somebody's] oversized accessory part) look about as large as the helicopter! (Indeed, next to the crew figures, the missiles look like IRBMs and the launcher appears not even to have enough clearance to turn.)
In any case, there are better solutions available - courtesy of another "trick": that many "1:700 scale" parts are in reality 600-scale, in size! This is particularly true of SkyWave weapons sets, for which I have verified several of the Late- and Post-WWII parts are indeed a perfect 1:600 scale. And with the abundance of nominally 700-scale USN Cold War kits on the market, I am sure you could come up with all desired accessories, in 600-scale.
Also, that square cube-looking Gun Director atop the bridge is undoubtedly meant to be a Mk37 Director - so much better-depicted by the 550-scale Matty's Models Mk37 Gun Director, or the "Boxy"-Type Mk37s, if appropriate: either of these being only 9% undersized for your king - and thereby well and truly "close enough", Daniel!
If you want any help shopping/obtaining any of the above type of smaller-sized replacements, just let me know, buddy.
Meantime, Great submission to ModelFleet - Thank You, sir!