This seems rather odd to me, since Kenwood designed the TS480HX 200 watt mobile to be powered off an automobile starting battery / alterrnator configuration
Not so much if you understand how batteries are made and the sub types. You are referring to Automotive Cranking batteries designed to deliver extremely high short burst of current and recharged extremely fast, then float as the alternator supplies all electrical energy when the engine is running. If you see a battery with a CCA or HCA raring you know instantly it is a Cranking Battery and the last thing you want for cycle service. Deep cycle batteries wil not have any cranking amp specs, only Amp Hours at various discharge rates. Hybrids will have dual rating, but not deep cycle FLA batteries. Hybrids are typically AGM jelly roll design for the top performers like Concord and Odessey.
You want a true deep cycle or what is known as a Hybrid deep cycle like a Marine, Solar, or RV batteries. Deep cycle batteries have much heavier thicker plates that completely fill the battery jar to obtain the capacity and material required for numerous recharges and AH capacity. This limits the surface area of the plates and results in higher internal battery resistance which limits current. Whereas a cranking battery has more thinner plates that do not fill the battery jar to allow for debris settlement. The thinner the plate, the more you can put in the jar to increase surface area lowering internal resistance and allowing much higher currents at the cost of capacity and cycle life.
For deep cycle and hybrid batteries, you want to limit discharge rates to no lower than C/4 (AGM) to C/6 (FLA). Otherwise, you will have excessive voltage drop greater then 1/2 volt. For a 40-amp load demands at least a 160 AH AGM battery, that will be discharged in 2 hours at a C/4 rate. Sure, a car battery can deliver 40-amps without excessive voltage sag for a few minutes until exhausted. Cranking batteries do not have many discharge cycles, they are not made for it.
Get yourself a good Marine or RV battery. with a proper float charger of 10-amps.