I'm confused. Do you have a 250? The starting battery isn't relevant.If the fridge lives in the vehicle full time from experience the 500-720wh (specifically the EcoFlow River Pro that can charge up to 940 watts) is the sweet spot unless you live somewhere cold.
The small power stations cannot handle 24hrs in the Southwest. Unless driven daily/fully charged in the afternoon.
The problem with a LFP swap, is unless you have one specifically made for replacing a starter battery like the very expensive Dakota it won’t provide enough voltage to fully charge the LFP.
With the available space you’d still have less capacity than a standalone unit.
You can add a low voltage cutoff before the fridge and dial in the voltage.