Apart from wanting to cut right through the board, it sounds like you want to achieve an inlay effect. For my money, I would settle of going the inlay route, working from each side but cutting and inlaying a maximum of 1/8in deep.
To do this you need a home made template for the patterns you want, and an inlay kit. The kit included a small bit (typically 1/8in) a template guide, and a spacer that fixes onto the template guide. Many suppliers produce the kits and most have web videos on using them.
In use you cut the recess and the inlay piece using the same template, and adding or removing the spacer to the template guide ensures that the inlay and recess match, unless you have sharp corners, where the recess will have a corner radius equal to the bit radius. In that instance you can trim the corners of the recess, or round the corners of the inlay to match. Here
is a link to a video explaining the method.
If you make the master template reversible, you should be able to get a very close match for the inlays so it looks as though the go right through the board. Hope this helps you.