You all are making this too hard.
Two pieces of wire, each ~25” long (standard dipole equation, total length (in ft)=468/freq in MHZ). In a perfect world feedpoint impedance is 75 ohms, but for us this is close enough to 50 ohm coax that the difference is not measurable.
Piece of coax connected in the center, one wire to the coax shield, one to the coax center conductor. Don’t bother with a balun.
Stretch the wire out from the center point - and it is fine to have the end droop down. So running this along the top of the fuselage with some tape is a simple approach. This now “inverted V” antenna also receives better on the sides than a horizontal dipole.
Don’t get wrapped around the axle on vertical vs horizon polarization. While this does make a difference in a perfect world (as in 100 mile range to hear a VOR instead of 60), for testing any resonant antenna is fine. Rubber duck type antennas however have an amazing amount of loss (there is no free lunch) but should pick up close VORs.
Carl