Don't forget to also add a switched "pre-charge" line, with a moderate-sized resistor, to handle the initial "rush" of current to charge the Inverter's capacitors. Without such a pre-charge circuit, you will probably blow your fuse or exceed your BMS limit.
LFP batteries have extremely low resistance, and the pair of BMS units doesn't add much either. A 3000 watt inverter can pull MUCH more than 150A (maybe as much as 400A?) for a very short period of time, right when you turn it on.
The resistance need not be very high (25 or ohms should be fine). But it does need to have considerable power handling. I use a 50W, 25 ohm wire-wound resistor, which was built into a small heat-dissipating aluminum case. (They cost less than $5). I also have a high-capacity dual battery switch (#1 - Both - #2) to activate the small-wired "pre-charge" circuit first (it's only AWG-10 fused for 30A), for just a second or two. Then I switch through the "Both" switch position, in order to reach the main-line-alone "Battery #2" position before turning on my 120v equipment.
In general, you don't want EITHER blown fuses or BMS over-current invoked and shutting down. The more likely cause of over-current in your configuration is the capacitor pre-charge and current rush-in - not your 120v load. There are several posts and even a video on this subject - search is your friend, if you need more information.
