Try a very slim strip of wood veneer between the bottom of the saddle and the pickup - works sometimes. More risky is looking under the pickup element, as it may not be sitting evenly in the slot - but there is an element of risk when lifting/moving the pickup. They can be very delicate, especially where the wire joins.
Another option is the K&K Pure pickup which glues under the bridge plate, inside the body. A more woody tone, and could be connected to any existing internal preamp?