The battery inside the BD power unit is likely very similar to this 18Ah AGM battery.
https://www.amazon.com/ExpertPower-EXP12180-Rechargeable-Battery-Bolts/dp/B00A82A3RK/ref=sr_1_1?ie=UTF8&qid=1481499823&sr=8-1&keywords=Ub12180I would be surprised if that battery could even support running an AC compressor fridge for more than an hour through an adequately sized inverter.
And Ciggy plugs and receptacles are an insult to 12vDC electricity. Passing more than 60 watts, it is but a matter of time until failure, and they will waste battery power as heat until that failure.
