A simple estimate of the power is quite easy actually.
120V @ 3.7A (PC) = ~ 450Watts continuous power while buffing.
Preferably you would need double that (900 watts) but you probably could get away with a quality 750Watt unit.
The
UDM is higher current so you would want to go with the 900W unit instead.
These units would need to be connected directy to the battery since the cigarette lighter can only supply ~ 150watts max.
Be aware that the elcheapo 1200W units for $49 are usually WAY overrated and can only supply that amount of power for brief moments or they'll blow up and possibly take out whatever is connected to them (PC or car battery or both).
Also keep in mind that at 400Watts you're drawing over 30 amps from the battery.
Not sure how long your could do this with the engine off before needing a jump start.
You might be better off with a small gasoline powered generator.