If the BMS has issues with tripping, it might be possible to increase the tripping point or even disable the over current protection. Since the thing won't have to run very long, FET heating on the BMS shouldn't be an issue.
Also keep in mind a typical lead-acid car battery has somewhere around 50Ahr or more of capacity. If you want to run your audio system or lights with the engine off for any length of time, you need a decent capacity. A 10Ahr lithium battery might start the engine, but won't run the other loads for very long.
"One test is worth a thousand opinions"