Inverters are not 100% efficient. That's why they get hot. If you're lucky a "good" one might be in the range of 95% but the cheap ones are more like 75-85% or so.

That means that your 300W inverter (output) will put out that amout of power but draw quite a bit more. So....your calculations 300W = 120V x 2.5A on the output side are correct. However, in order to generate that amount of power you're looking at 300W = 12V x 25A. Once you factor in this efficiency loss youre' gonna be right at 30A draw.

You should be OK but the best thing would be to get chargers made to use a 12VDC input if possible. Starting with 12VDC, converting it up to 120VAC, then back down to some charging voltage is a lot of conversion and you lose a lot with each process.