This sounds a lot like the LCS without the speed requirement, so maybe it ends up designated as an FF or FMS (frigate minesweeper) unless Rumsfeld is set on creating an entirely new hull classification. The La Fayette class sounds pretty similar in terms of basic requirements, although this FMS would have a larger hangar and flight deck. The La Fayette class, its international variants, and its successor FTI are all diesel powered, so that might give you enough speed for the littoral MCM/ASW mission. Alternately, a gas turbine CODOG system might be necessary for the speed to operate with a CSG. A ship of this size would also provide an easy path to upgrading the design, or maybe even existing ships, to NATO light frigate standards with ESSMs and Harpoons/NSMs.
Although I think cutting out the speed requirement and focusing more narrowly on the MCM mission would help move up the IOC, the lack of area air defense capability still puts the Navy in the same situation as it saw with the OTL LCS program. I don't think a 3,000 ton hull would be big enough for an SM-2 system and the helicopter hangar, so we might still end up having to switch to a larger FFG hull.
It's Rummy, so a new hull classification would better sell it
If you have an ASW variant that carries an acceptable towed array, you want to be able to operate with a CSG. I was assuming Harpoons but forgot to mention them, VLS more questionable as you need more than just free deck space and I think you want costs down to an absolute minimum to get as many as possible, even if I usually would favor leaving space free for that, though its topweight and power for the radar that's more concerning
The situation would be somewhat better as you have more hulls than OTL, with more up time per hull, so you end up easing some burden on the DDG's, ensuring more availability and reducing the maintenance backlog
Anyways I imagine it as something like this
FY 2005-2017 standard FFL/FFL(M) variants
FY2018-2023 Stretched FFL variant with a better radar and VLS for ESSM (and probably other stuff, whatever replaces RUM-139, LRASM, etc)
FY 2024+ A proper FFG, but since you have some sort of frigate can take time for a 7,000+ ton clean sheet design with room for upgrades to stay decent until 2070+ rather than the Constellation which while good is still somewhat rushed and has less growth potential being based off a hull first laid down in 2007