Phil,
Your history/nomenclature for Mk 37 director radars is a little off. My tutorial is focused on USN destroyers, but the Fire Control Radars used on Mk 37 directors on any USN ship were the same (different Mods maybe).
The Mk 37 director true enough didn't have radar when first introduced on the SIMS class destroyers. But, the first radars installed on destroyer Mk 37 directors were in September 1941 with the first being the
FD (Mk 4) radar. The Mk 4 radars were improved with various mods until replaced with the Mk 12 radar in 1944 on new construction.
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Mk37Mod22wMk4-3Aug42.jpg [ 134.98 KiB | Viewed 2851 times ]
The
Mk 12 radar was intended to be paired with the
Mk 22 "orange-peel" radar to improve low altitude performance and better height angle determination on the "Square-Backed" Mk 37 directors. The Mk 22 radar development lagged behind the Mk 12 by a few months, so some destroyers (unsure about cruisers, etc) went into service without the Mk 22. Most however had the Mk 22 added during Post-Shakedown. The
Mk 12/22 radar pairing was common on most USN ships with Mk 37 directors by the end of WWII.
Attachment:
Mk37Mod22wMk12-22-15Oct44.jpg [ 142.99 KiB | Viewed 2851 times ]
The late war replacement for the Mk 12/22 radars was the
Mk 25 radar, not the Mk 28. The
Mk 28 radar was a smaller radar (with a smaller dish antenna) intended to be installed on the destroyers with the older "Taper-back" Mk 37 director that couldn't accommodate the Mk 12/22. The Mk 28 was installed on SIMS-BENSON-GLEAVES class destroyers and GLEAVES class DMS units and some older destroyers with earlier directors.
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Mk37 wMk28radar-Jun50.jpg [ 148.68 KiB | Viewed 2851 times ]
The
Mk 25 radar didn't finish development until post-WWII and started to see fleet-wide installation/replacement for Mk 4 and Mk 12/22 radars in about 1949.

I don't have an Armament Summary Listing for any of the CLG's, but here is one for CAG-2 in 1960. As you can see she had a single Mk 25 radar that were installed on the Mk 37 director and six Mk 35 radars installed on the six Mk 56 GFCS.
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docArmSum1960-p96.jpg [ 150.36 KiB | Viewed 2851 times ]