Back to the Type 308 transmitting antenna.
Peter Clukey from Lockheed Martin confirms that the 649/749 Parts Catalog states that this feature was unique to Qantas aircraft 2562, 2565, 2572 & 2573 (VH-EAA to VH-EAD).
Earlier I searched for this type of antenna on other operators' Connies but couldn't find any. I then widened the search to look for the companion Rebecca antenna on the side of the nose. I found only one, on BOAC Connie G-ANNT. However this aircraft appears not to have any sort of antenna on the tip of the nose.
While we have solved the original Qantas problem, some may feel that we now have a BOAC problem. I'll leave that to our learned colleagues to ponder.