How is the roof performing now? Do you have to design for a snow load?
Consult a span chart, but off the top of my head, for SPF 1&2, for 2x6 rafters, 16' oc, I think the spans are something like 14 1/2' span for a no snow/no drywall/no attic, 20/10 loading. If you up that to a snow/drywall/no attic 40/10, the span drops to around 10 1/2'.
Look in the books for the hard numbers.
I your existing spans/loads are good, doubling up every rafter may be overkill. You can double every other one for added strength.
The cross pieces that you want to add are called "collar ties". By tying the opposing rafters together, the collar ties add strength to the rafters as well as help prevent the roof load from splaying the building's walls apart.
Garages have to meet certain restitions for fire code. Consider using 5/8ths inch "X" drywall. Sometimes referred to by the yards as "fire board" or something similar.
By adding the collar ties, they now become part of the framing of the garage. In my area, they would now have to be protected by the sheeetrock, thus, the drywall would be screwed to the bottoms of the rafters and the bottoms of the collar ties. Besides, cutting in the rock on the rafters and rocking around and on the top of the the collar ties in order to leave the ties exposed would be somewwhat of a pain.