all my other bikes have rigid frames so I can judge what the difference is. I was always dissatisfied with the wobbling of the SQ 4 after a bump.
At first I loosely fixed the friction dampers and braked with the rear brake: the usual jiggling *). Then I hopped over the selected bump (ugly railroad crossing): the usual jiggling.
In three stages, I then gradualy adjusted the friction dampers and made each of the tests as before.
Result for me : Significant improvement in behavior, comes close to the rigid frame with the difference that you have (some
*) There is also some movement "Feeling" at the fork at the begining of a hard front braking, it is the same for the Ariel as for the BSA
I got used to it
1923 James Model 12 500ccm v-twin -- 1960 Chevrolet Corvette C1
1926 Douglas EW 350ccm flat-twin -- 1967 Chevrolet Corvette C2
1936 Motosacoche 500ccm single --- 1979 Chevrolet Corvette C3
1948 BSA A7 500ccm parallel twin -- 1955 Ariel Square Four MKII