Hola Uzzy!
I think the issue with the membrane has nothing to do with the lever moving towards the grip during constant braking.
It is more likely that the primary seal on the piston of the brake lever is damaged. When pulling the lever the primary seal passes the sniffing hole and engages the high pressure system of the brake. If the primary seal on the piston is leaky, oil may pass the seal and this causes the lever moving towards the grip during constant braking. The effect should not only appear when riding but also when standing still and constantly pulling the lever.
I think the issue with the membrane has nothing to do with the lever moving towards the grip during constant braking.
It is more likely that the primary seal on the piston of the brake lever is damaged. When pulling the lever the primary seal passes the sniffing hole and engages the high pressure system of the brake. If the primary seal on the piston is leaky, oil may pass the seal and this causes the lever moving towards the grip during constant braking. The effect should not only appear when riding but also when standing still and constantly pulling the lever.