The inverter fuse is questionable. Using the divide by 10 rule where 1500w will draw 150a and you want a bit of margin. Then there is the surge for the inverter (3000w?)
Ihe inverter installation manual should specify what fuse it needs for max draw on the batteries. If you never plan to do that much you can get away with a smaller amp fuse.
EG my Vector inverter manual says for a 1500w version of their inverter, where they account for the 3000w surge, it should have a
300a ANL fuse on #2AWG up to 6ft long or else use 2/0 up to 10ft.
In real life, I have their 2000w which calls for a 500a ANL, but I only use 300a because I have no loads that need bigger.