Thanks for the further comments and advice, Gents.
Mike: I have had the 2nd I.F. can out of the set to recover the core assembly which dropped down into the coil former when I tried to turn the adjusting screw. I can't see any terrible crime in fixing them with a resin glue once they are accurately setup. Re-adjusting I.F.s is not normally a regular operation, and if they are set correctly they shouldn't need to be disturbed again.
Sideband: The adjusters on this set are not set in Bakelite, if they were I doubt I would be having all this drama. They are going through a couple of layers of Paxolin sheet, into which I suspect that they cut their own threads when first fitted, in the manner of a self-tapping screw. The core (unintended pun) of the problem is that the paxolin has become friable due to it's age. So the threads of the adjusters no longer grip on the paxolin. I shall re-align them with the set in such a position that the I.F.s are horizontal, and then fix them before standing the set upright again, thus defeating the effects of gravity.
Other things press for my time, but I hope to resolve this problem quickly, and will report results, hopefully, very soon.
Thanks for the helpful tips.Tony.