Sorry for taking so long to get back to you on this one.
What you really need is a lead-out move. CamBam supports lead in moves, but lead out moves are currently still on my todo list, but should hopefully appear soon.
I had a go at trying to do this manually with mixed success. As you suggest, I used another drawing object so that when the toolpath finished a circuit of the main object, it then moves to the other object which leads the toolpath away from the main surface.
There are a few things to consider though.
The extra shape needs to be big enough to generate the same number of cutwidths as the main shape.
It needs to be positioned near the starting point of the main shape - this is indicated by the position of the direction arrows on the toolpath.
LevelFirst CutOrdering must be selected.
I have attached a file to illustrate this. Hopefully it will do what you need.
The melting plastic does sound a bit worrying though. You might try turning your spindle speed down as slow as it will go and increasing your feedrate as fast as it will go and use light passes.
Another thing I found very good for cutting plastics with fast spindles, is single tooth TCT wood router bits. I got them mail order from screwfix and they were very cheap.
Good luck with Mk II !