Ray:
That would work OK. I recently worked on a large motorsailer with just that configuration (copper strips in the overhead).
Signal strength would probably be as good as if the strips were lower in the boat -- underdeck or in the bilge area. Only thing is you might have more interference that way due to the interaction of rf with other wires and devices nearby -- both on transmit and on receive.
But, if that's the best you can do, try it. You might actually do a trial by just taping the copper strips to the overhead, without fully installing them. That way, you could experiment a bit with numbers and placement. Take time doing this. Check out several bands, and do it on different days to account for unusually bad (or good) propagation conditions.
Finally, if possible it would be good to run a copper strip....or a heavy wire...from the tuner ground lug to the nearest bronze thru-hull. This might help cut down on the noise a bit.
You never know for sure what's gonna be best. I asked a boat in the Bahamas yesterday what type installation they had....boat checks in every day, and has a strong signal compared to other boats in the same anchorage, and general area. Answer: a M710, backstay antenna, AT130 tuner, and a 20' long heavy wire running from the tuner ground to a ground plate. All some 13 years old!!!
Bill