Is the same volume of 1oz copper over 2x the area approx. equivalent?
It will not quite be as good, as the heat needs to travel sideways, but a larger board will radiate more heat into the air than a smaller board.
PCB houses tend to charge an adder for 2oz, so most prototypes use 1oz copper.
This design is not many-watts so you should be ok.
In your design I might duplicate the power copper areas on the reverse side, at least for 20~40mm, and add thermal vias to those areas.
The heat then transfers across a larger area to the larger GND planes.
Also, place the thermal vias closer to the SO-8 package. You want both side to be working for you.