I've met the guys at PBE; delivering and collecting a servo for my dad's '46 Chevy truck (I lived in San Jose at the time). I met the tech that rebuilt Dad's servo (he had a Girling, from a Jag, IIRC, on his bench). Their shop is pretty grimy, as you'd expect, but they were quite cordial, you could give them a call and see what they suggest, they may have some 'tricks' you could try.
There are three cylinders in a Girling servo, a master that operates a slave cylinder which operates a T-valve that gates either vacuum or ambient air into the large piston in the canister (technically, a cylinder). Which one do you think is stuck (probably the air/vacuum piston, but the hydraulic section could stick as well)? If you have the Mk IIA servo you can open up the air/vacuum canister--you might damage the gasket--and see if you can persuade the piston to move (but the PBE guys probably wouldn't touch it after that). The air/vacuum cylinder/canister is lined with a dry lubricant that could be worn causing the piston to stick, and sometimes the leather seal will stick if the rubber tubing backing it up is cut too long. Either/both of the hydraulic seals could be stuck as well, as could the 'gland' seal that seals the rod on the air/vacuum piston (they're what often gets brittle and fail, allowing brake fluid to get sucked into the intake). There is also a check valve on the vacuum inlet, which permits some assisted braking if the engine quits, but shouldn't otherwise affect operation of the servo.
I've successfully rebuilt a Mk IIA, but gave up on a Mk IIB when I lost some parts.