I didn't think they would work because I'm using big cables with alligator clips to connect the battery to the inverters.
Maybe it is time to dial in your setup a little more. Get some ring terminals, splices, and spade connectors and a decent crimping tool and you could easily redo the wiring. If you have an extension cord laying around, you could harvest wire from that, but you can also buy wire so that it is the right size for what you need. Every wire that connects to a battery's positive terminal should have a fuse on it sized to interrupt the largest current that the wire can safely handle.
For a 400 watt inverter on 12v that would be about 33 amps (400W/12v = 33.33A) 10 ga wire would be ideal, although for short sections of wire in free air 12 ga or even smaller could probably still work.
If you are running only small loads, then 400 watts is probably more than you actually need. Larger inverters tend to have larger idle current draw. If you are trying to keep your system very lean, then I would suggest you get one of these:
https://www.amazon.com/Digital-Battery-Low-Voltage-Protection/dp/B07929Y5SZ/ref=sr_1_1?dchild=1&keywords=12-36V+Battery+Over+Discharge+Low+Voltage+Disconnect+Protector+Modules+DC+Output&qid=1632339115&sr=8-1
and put a 100Watt inverter on it. (note that it is only rated for 20amps, so MAX 240watts) Really, you dont want to discharge a lead acid much beyond 50% - so once you get under something like 12v you are shortening the lifespan of your battery quite significantly. At 11.5v, it maybe has 10% of its capacity left. You could even get a 2 pack of protecting circuits for a dollar more, and set them to different setpoints. Have a big inverter shut down at 12v, and then limp along on a smaller inverter until you get to 11.5v. If you cycle below 50%, you can probably only count on about 500 cycles before the battery is toast. If you routinely take it down to 10%, you will be lucky if it lasts a year.
Edit: if you really want to run a bigger inverter, here is a cheap work-around: Get the smaller protecting circuit, and wire the "load" to the coil of one of these:
https://www.amazon.com/Continuous-Solenoid-Nickel-Plating-Lucky-Seven/dp/B0859BZJNW/ref=sr_1_3?dchild=1&keywords=50+amp+solenoid&qid=1632339700&sr=8-3
Then wire a positive cable through a large fuse and then through the big posts on the solenoid to the inverter. That should let you run anything up to 3600W.