Hello and welcome to the Forum Jim. A very interesting back story to your radio there re the Dr Wadley connection. I'm sure someone can advise your re the broken whip aerial but I doubt that the length will be that significant in terms of reception-practicalities must limit these to a couple of feet in the end. If you are looking to tidy things up with an unbroken whip though, it may be possible to source a replacement or something very close
Of course, using a long wire and earth/ground from the sockets-possibly via an ATU [Aerial Tuning Unit] is likely to bring the best results. I'll leave it to others who can offer more exact advice, particularly re picking up on Air Band Transmissions via the Sangean. I once got a Pilot [out of Gatwick] calling for assistance on landing re a passenger who appeared to have broken a leg... actually on the aircraft!
I've got a JRC 515 [Rolls Royce but not in use at present!]
Dave W
Bexhill