^^
Apart from that you'd need to insert the shim at the heel end (not the body end) of the neck pocket in order to get the neck pointing down towards the bridge more.

A shim at this end of the pocket isn't desirable IMO, but it will give you an idea of how much the neck angle needs to change by. I'd then re-angle the bottom of the neck, but it's not an easy job to do well and keep the bottom flat without curving the edges.

So you may want to stick with a shim, but it's going to be visible at the heel end, whereas one at the body end won't be visible.