I have done some thicker stock and just used CW to outline the pattern on the thick stock by assigning an 1/8 in straight bit to it and cutting a shallow path.
Used the band saw to cut it out and had a good line to follow.
The router and jig method works well just takes longer and you need a long flush cut strait bit in a plunge router.
your call but the band saw is much faster than the CW on cut outs
Brent
A,B machines, PE,probe,conforming vectors, centerline, 2d,3d,stl and dfx imprt, rotary , 3.xx, Pattern Sculptor
OS X Yosemite
Woodwork is what I do to pay for my tool addiction.