I am not a SprutCam user, but I don't know why you couldn't run both sides of a part in one set up.
For the first side you would use G54 coordinate with tools T1 through T10. For side 2 You could use G55 and tools T1 H11 through T10 H20.
All the tools would be the same for both sides of the part, but the offset lengths would be different. T1 H1 (T1) would be used on the first side of the part and T1 H11(T1 with a different offset) would be used on the second side of the part.
Russ is right though. If you're going to make a bunch of parts, you'll be WAY better off to run all the parts on one side before you flip them over to run the second side. That would be way less confusing.
You can buy GOOD PARTS or you can buy CHEAP PARTS, but you can't buy GOOD CHEAP PARTS.