I assume that there is still a coax cable running through the car and to the rear window where it's connected to the upper window elements.
Surely this could be intercepted and connected to a rear whip aerial with comparative ease ?
I'm afraid it's not that simple... The cable which runs from the head unit to the rear screen is not directly terminated with the antenna wires in the screen itself. It actually connects to a small amplifier on the left side of the screen. This then has three flying leads coming out of it which connect to spade terminals attached to the antenna patches printed onto the screen.
I've had radio reception issues from day-one, and have had no joy in getting the dealer or Honda to solve the problem ("Your radio is inside the allowable specification sir"). It's been into a car radio specialist in Cambridge (at my dealer's expense), who were amazed when they realised that they could disconnect the antenna patches from the amplifier with no audible change in the signal. However, disconnecting the amp from the head unit (at the amp end) causes the signal to drop, implying that the wire between head unit & amp is OK. Their original plan to diagnose the fault was to do as you say, i.e. connect a normal antenna, and see if it improved things. However they binned that as an idea when they saw the amplifier.
The trim panels to expose all of the above are currently off my car, with a view to doing a bit of experimentation attaching lengths of wire in place of the rear-window antenna patches. Hopefully I might get around to this in the next few days. I don't hold out much hope for it as a solution, but there's not much else left to try.
One thing I seem to remember reading about was that the head-unit to amplifier cable runs up the passenger side A-pillar, and can get trapped/squashed by the trim. Has anyone any experience of this happening?