6000 ac watts / .85 conversion factor / 43.6 volts low cutoff = 161.899622234 service amps
161.899622234 service amps / .8 fuse headroom = 202.374527793 fault amps.
You want to bump that wire size up to minimum 1/0awg and use a 250 amp fuse.
The wire should be pure copper with insulation rated for 105C.
4x 100ah AGM batteries in series is not enough to feed that LVX.
They would be able to feed that all_in_one flat out for ~30 minutes and the peukert effect will be brutal.
I'm not sure what 400 watt means in the context of an agm battery, please explain.
I'm not experienced with AGM batteries so I will have to take your word for it that 43.6 volts is an appropriate disconnect.
My gut says its too low.
As above I suggest 1/0 awg with a 250amp fuse.
Nope, class -t is not required for AGM batteries.
Also since they are in series they are treated as 1 battery.
I suggest a 1 of these
https://www.waytekwire.com/products/1646/Bolt-Down-Fuses/&Series=MRBF-Series&Current-Rating=250A
On 1 of these
https://www.waytekwire.com/item/45567/EATON-s-Bussmann-Series-MRBF-Mounting-Bar-3-8-/