One reason I wasn't sure about the "ribbon" was that the photo of the Branch shows a laurel wreath with the 'insignia' inside , why not just use an actual ribbon ?
The later BLESMA badge and crest have a sun with "four crutch-heads" to " represent limbless service personnel from the four services united in the Association".
My first imperssion when seeing the Branch photo was that it could 'possibly' be meant to represent a chair with crutches/walking sticks for handles ?
Early WW1 era wheelchairs were basically standard 4 leg chairs with side wheels attached.
Four services (4 legs) crutches/walking sticks (disabilities) ???