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When I brake hard I squash my two little fingers which means I can't get maximum braking power without using 4 fingers - which I do not like doing.

The lever APPEARS to have an adjustable slug which presses the hydraulic plunger, but it is also stuck fast, does not appear to have a full slot for a screwdriver, and I hesitate to apply torque to it if it isn't adjustable there.

The manual does not appear to have any process detailed to set the lever distance.

Any and all advice gratefully accepted.

Yes, it's adjustable, but rust might have corroded the slot.
Anyhow, this will bring the lever close to the handle, and will not improve the breaking effect.
newer and softer pads or stainless pipes will help. In case of a bigger effort, you can also put a radial brake pump