Your inverter figures seem MASSIVELY over-rated - why are you using such big ones?.
As for your lights?, why don't you use better lights - what are you using?.
Run current is only 1.4 amps on the tiny refrigerator but start up current trips the 300 watt and 1000 watt converter. It seems to me the refrigerator would run on the 300 watt converter if I could figure out how to get the frig started. Surge current must be more than 8.3 amps on start up.
I have the same problem with the electric chain saw surge current trips the 300 and 1000 watt inverter.
The electric coffee maker is 600 watts, electric griddle 1400 watts, computer 400 watts, in the camper trailer. Lights will run for a week on the battery without charging the battery. I have 3 lights inside the camper 25 watts each, 1 light outside 25 watts. It does not take much power to run the camper trailer lights, the 400 watt solar panel and battery work GOOD. I like to cook outside on the picnic table using the Coleman camp stove, rarely use the electric griddle or electric coffee maker. I have to be careful how much power I use and keep a eye on the clouds and sun to make sure the battery is staying charged. Sometimes after a week of camping the battery is dead, problem is mostly too much shade from trees.
This 400 watt system will not work at MY home, refrigerator is much larger, TV is larger, AC unit is large, kitchen stove, hot water heater, when I use them, they all trip the 1500 inverter but would probably run on the inverter if I could get the items started. The surge start up current is the big problem for AC and the refrigerator. We have 2 computers, lots of kitchen appliances, lights, TV, this all uses massive amounts of watts. I need about 6kw at home. If I could do without the AC unit, electric stove, electric hot water heater, I am guessing 2000 watts will run the house.
I tried to run my house on a 5kw generator it will not work. Every time the AC unit comes on the generator over load trips. Kitchen stove trips the over load too. A few lights, TV, and computer will run fine until the kitchen refrigerator comes on then it trips the 5kw over load. I need to experiment with a 6kw and 7kw generator to see if it will run the house without tripping the generator over load. Probably the smart thing to do is rent a 10kw generator with a meter that reads how much power is being used but there is still the problem of how to read start up surge current for things like AC unit and refrigerator. An amp clamp that reads peak demand might work.
All my inverters use power from the battery when they are turned OFF and still connected to the battery. I need to make sure they are never connected to the battery if they are not being used. I have not checked to see how many amps the inverters use but the small 300 watt one will kill the life of the battery in 2 days if I forget to disconnect it when not used. I use the 300 watt inverter 98% of the time. Only time I use the 1500 watt inverter is when I use the chair saw. We never use the refrigerator it kills the battery very quick. The generator circuit breaker is 20 amps 240 vac, the house circuit box mail breaker is 200 amp 240 vac.
If you buy an inverter test it to see how many amps it uses connected to the battery. Maybe you can test several inverters to see if they all use amps while connected to the battery. Maybe certain brands or newer models are better. It sure would be a BIG advantage to find an inverter that uses no power when it is not being used.