You may find that your Axis already has a neck shim, if so, experiment by placing another within that is thinner. Do it gradually though, as small amount goes a long way and makes a huge difference. If there is no shim, then there is some shaving of wood required (neck or body, i'm not sure), perhaps. This i have not done and i would strongly recommend contacting customer support before doing anything like this or a good luthier as "the shaving" is an irreversable process. Though it too can be remedied by shimming.
Hope this helps! Others may chim in with their experiences...
that's the ONLY way I set action on all my bolt ons; tilting the bridge and truss rod adj. is for "normal" general players and is suffice for general set ups".
To get "precise" top of the line professional level set ups does take some degree of technical skill, and I wouldn't learn it on an expensive guitar.