Haven’t addressed Galrahn directly on this yet, so i’ll do it here and now…
well, i think Galrahn reads here too.

Not to mention you’d get a fairly big ship for $100 million if you kept it simple, bigger then 1,000t anyway.

Only if you go with commercial standards. Typical offers in that range with COTS equipment are large corvettes or OPVs in the 2000-2500 ton area such as BAM or probably a Thetis, even though that’s both already slightly above the mark.
When going with military technology, even OTS, this becomes vastly pricier. $100 million for a “mixed” ship using some COTS equipment in the 1000-ton range is reasonable.

1,000-ton patrol corvettes are sound for the purpose in a littoral-only context; however, there are obvious limitations to the concept, such as range and transoceanic transfer of a squadron. This is more of a question of machinery chosen though – sacrifice speed for range and better seakeeping. And, of course, the likely lack of organic helo support – there are few ships in that range supporting helicopters, unless that’s meant as one of the key purposes of the ship (such as in the USCG Reliance class WMECs) . They’d likely have to be semi-permanently forward-deployed, like France does it.

Using the LCS as a command ship for such a patrol squadron… well, sounds like “we have to find a role for the LCS”. Why not a slightly bigger, dedicated ship that could also provide enough replenishment for tripling endurance, some crew relief, a dedicated command system – and is likely considerably cheaper to build? To be fair, i think the LCS could make a relatively decent ship in that role too, if you have to use it.

I’d question the use of two modified T-AKE (40,000-ton ships at a cost of 400 million per!) for supporting the whole squadron. Only 3400 m³ DFM storage total either – even German tenders (at the level of the LCS here) already carry over 500 m³, and that’s before dedicated replenishment ships come into play.
Perhaps adapting the two laid up cancelled Henry J. Kaisers in the NDRF as a multi-purpose single-ship support base would be viable in this regard, converting at least half of their fuel capacity into dry cargo and ammunition transport. Pair them up with LPD-17s or a derived ship, give them an escort or two, and done for the “mothership”.
With the 16 PCs, 4 LCS, 1 LPD-17, 1 HSV, 1 Burke, there would be around 2500+ people likely to be supported (regarding food etc). I think this could be done with a single modified HJK for a number of weeks at least still.

I would perhaps add a second HSV.