Don't forget the other metal
"...In my Boredom Fighter ( fuselage now ready for covering - hence urgency to deal with the antenna installation ), the rear fuselage is a mess of cross members, control cables, trim cables and more cable for the locking tail wheel. There has to be a large "V" shaped zippered access panel in the bottom fabric, to allow minimum access to the cables, turnbuckles and pulleys etc. This rules out a ground plane anywhere near that. ... The dipole can be fitted offset to one side so the lower element clears the control cables..."
Ian, the challenge I think you may have is that all those cross members (if they are conductors) and cables is that they form a distributed, but messy, ground plane, whether you want them or not. Running one leg of your dipole down among this "mess" will affect the performance of your antenna, both the loading that affects how much power gets out and the antenna pattern.
Jim Weir may have some other suggestions but in my opinion you might want to consider constructing a ground plane for a 1/4-wave antenna in your turtle deck and take the drag hit of an exposed antenna. Also, you mentioned constructing the antenna of piano wire. The bandwidth (tuning range) of an antenna is affected by the diameter of the radiating element. A piano wire antenna will work well at one frequency and less well if you tune to other frequencies in the VHF aircraft band.
Al Burgemeister