Any tricks to removing moulding with intent to reuse thus desire to avoid damage?

My base and my window trim were not removed when either 3/8 drywall or a layer of plaster was added over my shiplap, and the fact that the top of the base is almost flush with the walls doe snot sit well with my wife or myself.

In a not unrelated topic, when I put the base back, what medium should I put under the base to make the width look correct? I am leaning toward plywood so I do not have to worry about nailing the base back into the studs, but welcome any idea for a novice like myself.