You might consider adding something like this to your setup, a 12V DC/DC stabilizer/regulator, so you always get a consistent 12V output for your leds even if the battery voltage fluctuates a bit.

https://www.amazon.com/Voltage-Stabilizer-Regulator-Protector-Protection/dp/B08BRN3R5Y/?th=1

https://www.amazon.com/Stabilizer-DROK-Waterproof-Transformer-Television/dp/B081RG8XP5/?th=1

Something like this that has a wider input voltage range is what you want. I used a similar one and wrote a post about it. There is even a picture of an inverter hooked up to it.

I have the official Ryobi one and use that more than my homemade one, but I have it for emergencies.