You screw then to the studs through the foam with a screw with a completely flat head that can handle the weight of the siding, foam and furring.
HeadLOK® Heavy Duty Flathead Fastener - FastenMaster
This way you minimize the penetrations. You could also run a bead of foam under the strapping so the screw will pull the foam through as it goes in. It's really a conundrum.
Apparently SimpsonStrongTie is making a competitor but I haven't seen them in the lumber yards yet.
EDIT:
It's 3M 8067. You should be able to get it anywhere.