Thats where I live! (Machen, not on the common). Ridden that 'road' on my Strom and DRZ a few times.
You have to be careful up there though, as technically there is no right of way (at least according to the information I can gather), and there has been a lot of problems with MX'ers so the Police have been known to patrol up there.(Having said this, if you are on a road legal bike, they would probably just laugh at you and tell you to go somewhere else)
You can go pretty much from Rhiwderin, along to Wylie without too much tarmac, and all doable on a GS, or a Strom.
Might have to join you boys for a ride sometime!
There are also some BOAT's on Senghennydd common, which are legal, and GS able, although a couple of sections are a bit muddy/rutty so you would need TKC's rather than road tyres.