Well yesterday morning was good. Yesterday afternoon and this morning, the legs have completely gone!!
In the good news, the work I did on the headset of the commuter had a positive effect so, having taken Lelly out on Sunday, I can confirm that both bikes are now operating silently and well. Only cause for concern remains the tyres on the commuter but I'm not getting visitations so I'll buy a couple as spares and see how long I can run the existing ones for.
Next job I think is to convert the SS to a fixie. I've accepted I'm never ever going to use it for commuting (the original idea) but I may as well try to get used to it.