Thanks everyone - very helpful. I was thinking I'd have to weld up the adjuster pistons.

The article I remember also discussed doing away with the alignment tabs, to allow easier fitting and improved location by virtue of a 2 BA (?) sprung retainer. More like a modern arrangement. Does this ring any bells?

I'm very flattered to be asked to contribute to this thread.
John Sutton was involved in developing the specifications for the Bespk Austin 7. The full story of the various mods are featured in an article in the BA7C..
Firstly the late iteration of Girling brakes on Austin 7's and Big 7's had a floating adjuster. This was achieved by using elongated holes in the backplates. In order to prevent the ingress of dirt I constructed banana shaped gaskets made of 30 thou SS sheet/shim stock (in fact from the duct for a kitchen extraction hood). The adjuster is fixed to the back plate with bolts Loctited in position but with 'Thackeray' washers (double coil spring washers) nipped up and then backed off so the adjuster can just slide/float.
The Girling shoes need to be modified by cutting the adjuster slot out (as at the actuation end) as one of the other contributors has suggested.
With this arrangement: the adjuster floating and the shoes floating the brakes can float into an optimal position.
This set up works extremely well.
Having been brought up on Austin 7's the use of brakes is only for extreme situations. When we got back the shoes were not fully bedded in: after 23,000 miles.

Location: Saltash, Cornwall

A few months back I was contemptuously rubbished for commenting that shoes radius ground off the car may not give immediate good bedding for a Seven although it is good practice with a modern.
For anyone who might be interested the full explanation lies in Guy Butchers description. Most other cars are arranged as the mod ie the shoes are free to move lengthwise slightly and the actuator can move circumferentially slightly. Thus a shoe accurately radius ground off the car can immediately find its ideal location. Whereas with the stock Seven the shoes are fixed endways and both shoes are each fixed circumferentially by the cam faces. Thus shoes fitted to the drum radius on the car, using sandpaper in the drum or similar technique, are much more likely to achieve an immediate bed.
Most cars have relatively flat surfaces abutting at the shoe ends; the mod had occurred to me but I suspected a modified Seven would soon develop a depression on the leading shoe and resist sliding.
One would reasonably expect the floating arrangement to be prone to grab and dragging and uneven wear but myriads of relative moderns operate with.(If anything gets stuck very irregular wear often does occur)

Location: Auckland, NZ

I am looking at my spare Girling hub assembly in the warm on my kitchen table and can see the logic of cutting the adjuster (slotted) end of the shoe horizontal to make it slide as required to find it's centre position. However, this leaves only one end of the shoe and adjuster touching. Will this not lead to early wear in the shoe stopping the very thing trying to be accomplished?. Would it not be better to elongate the existing slot (keeping the existing angle) enabling the shoe to slide as required plus biasing the shoe towards to the actuator end as at present. Or am I 'way off track' as usual?
Peter.

Location: Truro(ish)