The outer cylindrical skin must be cable of accepting/transmitting the deformation, and if there are no specific 'target' zones then, if not pressure based, then I could envisage a couple of other concepts: One method might be to have a length of spring steel sheet, like those used for lead-screw guards, one end anchored to the skin and the other, monitored, end to an arbor - as the cylinder is squeezed the spiral will try to wind up? Alternatively, I wonder what results you would get if you wound a lap of strain gauge wire on a compressible cylinder, just like a single-layer-winding solenoid; you would then face the challenge of slipping that inside a compressible outer sleeve and filling the annular void with a medium that ensured the pressure was transmitted to the inner cylinder & coil.... Or maybe there's no coil -might it be an air-spaced cylindrical capacitor - one plate = fixed inner arbor, other plate = deformable skin?
However, I've just been back to look at the pictures in the original thread - and there are specific two-jaw and three-jaw adapters with pads for the jaws to bear on. The adapters' purpose could be to avoid marking the head but they look to have sprung fingers with "pips" to engage in specific dimples on the measuring head; hence pressure will always be at the same specific points on the circumference - so maybe a set of six strain gauges and appropriate adapters could accept 2/3/4/6 jaw chucks?
So, maybe it isn't a generic "any point on the circumference" cylindrical strain gauge at all!
Dave