I hope you take a moment to reflect on the silliness of a '70s-'80s frigate attempting to have four missile fire control channels, one more than a Kidd of twice the displacement.
There is more to naval electronics than the antenna you stick on the top of a deckhouse, especially in that era.
Guidance channels are like money, sex and dakka. Enough is more than you've got, and less than too much, and there's no such thing as too much!
As for the Kidd, I never understood exactly why it did have so few. I always chalked it up to having originally been designed for Iran, but there is no reason it couldn't have had at least one more, especially on a hull that size.
Looking at revised possibilities, maybe a Spook-9 for the 76mm forward, keep the pair of STIRs where they're currently at, and replace the aft CAS with a with one of the little directors that can guide either the aft 40mm or the NSSM.
Plan B is would be to get rid of the NSSM completely, and add a couple more 40mm mounts, with a dedicated director.