Just some thoughts here:
Firstly, the House Wrap idea is a good one from several perspectives. It is a "membrane" that stops draughts, is water resistant, is water immpermeable, etc. Use it underneath regardless of the method you use to re-install the siding.
Secondly, about the fastening of the siding: I would be very tempted to strap the panels horizontally after applying the house wrap. The space behind the siding will keep the wood dry even if water leaks back there through the knot holes, etc. It is the reccomended method here in rainy British Columbia. The Prov Building Code requires the "drain and vent space" under wood siding, I believe. For any of you fortunate to have viewed or visited the Eagle' Eye Restaurant at the top of the Ski Hill during the Kicking Horse Bridge Project in 2001, that method was used to attach the siding up there. And drying out is critical above the treeline, since the hot season is so short.
Also, if the furring strips are well attached to the panels, I think nailing the siding to the furring strips would be a better method than nailing it to the exterior sheathing of the panels.
Another thing to consider would be to wrap the barn, attach the horizontal Furring strips, hang "black paper" vertically over top of the furring strips, then attach the siding. The Black paper is (relatively) inexpensive and would conceal any of the house wrap from showing through the defects in the siding AND provide one more layer of water / wind resistance??? It could be the light "tar paper" or the heavy "roof felt".
