One of the features of Syncronous is that (by and large) it deliberatly doesn't allow links between parts as this is a main point for failed features and long rebuild times etc.
Obviously this has it's downsides too, so I would use ordered for the job you're describing. In fact we do almost the same thing with steel and rubber. I'll often model a sheet of steel in synchronous, then do either a part copy of that into an ordered part, bringing it in as a construction body. You can then use the thicken function on a single face and select your thickness.
The beauty of this is that you can synchronously edit the steel part (wood in your case), and the rubber part (foam in your case) will automatically update to match the profile exactly.