How can I lift glued carpet without destroying it?
The answer to this was Acetone.

Turns out the carpet was glued to the gripper rods in the corners and every 30 cm or so along the rod there was another spot of glue. No glue to the floorboards.

Pouring acetone along the edge enabled me to lift the carpet fairly easily. It did cause some slight damage to the glue keeping the backing to the carpet and where the problem glue didn't quite dissolve well enough I got a few pulls but thankfully not too many.