The mini can be powered from 12 to 48v so that it can easily work on the DC systems in cars, RVs, and boats. Using an inverter to go from DC to AC and back to DC will introduce a lot of inefficiency as each time the the power is changed from AC to DC and back, it will lose 5-10%, so that is somewhere between a 15% to 30% waste of energy.
Wire the Mini to your DC system and use 10 ga wire and keep the run as short as possible as possible. If there are perfmorance issues, then get a DC-DC charger or a DC Buck Boost to raise the voltage to 24v. According to the specs, the Mini will draw from 25 to 40w, that's a max of 3.33a at 12v. According to the ABYC ampacity tables, 10 g is good for 60' at 5a for a 3% loss and 170 feet for a 10% loss. Don't use a cigarette lighter type plug they are not reliable.
If you don't want to cut off the end of the supplied cable, then oder a
12v connector pig tail (Amazon Link) and make up your own power cable. No need to over think this installation.