Moreover, the River class systems (weapons and sensors) have not been acquired yet, so don't exist.
However, while the hulls, propulsion and hotel services of the CPF's are quite worn out (and slowly dying), further to the FELEX program, their combat systems, sensors and weapons systems are quite good and ready to keep going for quite a while.
So, we get back to a solution I proposed some time ago: Find a modern hull, power plant and hotel service that is more modern, in the 4,000 t0 6,000 range, build them "as is" and move the weapons, sensors and combat systems - including the Ops consoles - to it.
I get back to the British type 31: Get the hull, power plant/hotel services and move the Sea Giraffe, SMART-S, sonars, electronic warfare, comms suite and ops console with CSS-330 into them with the weapons system (though, for the missiles, I would put in a short length VLS system) and you have your stop gap ship that can be built and hit the water in three to four years from now, with another one every year thereafter. Just have them built by a combination of Hedley and Davie (which is more than big enough to host both these and their Coast Guard icebreakers).