What I'll do at the week-end is drag the 15 clocks outside,  the only
place roomy enough at the moment, and set them all up on planks.
There will of course be brandy standing by for any disorientated
visitor who thinks they've walked into a Dali landscape. Might run a
sweep on how many times neighbours and car park patrons next
door say "What's the time ? ha ha". Haha, we'll see who's feeling
funny on Sunday morning after listening to 15 solenoids clumping
all night (nah, wouldn't really do that).

I'll try an LM317 first, as that's simplest, and perhaps even knock
the caps down to 1000u. The coils are nominally 24V but do work
from a weedy response at 7V to the maximum rating of 30V. 12-
15V is a convenient middle ground. Dropping the caps to 1000u
might mean upping the voltage, and that's a whole new ball game.
Some clocks will have 100ft of cable (figure-8 mains) on them so
that will have to be taken into account.

I saw mention of "ganging" two transistors, but couldn't find a post
where this was explained in detail. Could someone do the honours ?

Thanks for all the help and suggestions so far