4kw @ 24v nominal yields 167A continuous current. LFP nominal is closer to 26V nominal due to its nice flat curve. So4kw @ 26V yields 153A.
1200AH of lead is approximately 500-600AH of LFP.
What's your main charging source, Gen, PV, other?
Do you need redundancy such that each individual battery can carry the entire 4kw load?
The ~280AH aluminum cased prismatic cells are a good value currently. Here is my initial suggestion pending answers to the questions above.
Build 2 8S packs from 280AH cells. Each with its own 110-120A FET BMS. This is probably the cheapest route, and you have some redundancy, but you are limited to 2.4-2.8kW if one pack drops out.
This is only ~560AH nominal (504AH usable with conservative cycling), however with the higher charge efficiency, almost 1.0 peukert, and higher nominal voltage, you will have similar or greater performance than the 1200AH lead pack. 504*26V = 13.1kWhr, and all that is available, even at 150A rate.
Sourcing cells for best value typically requires you to buy cells direct from China via the grey market. These are typically ~B grade, which means they aren't perfect. Most of us have had good luck with these cells for C/2 rate off grid applications.