Ray,
Aside from the riving knife, I think the best safety device to come along in years is the GRRipper and I use one (or two at a time) whenever possible and this includes cutting thin strips.
For Southwest designs, I always cut out the center by putting one sawtooth edge against the fence and then turning the board around to repeat the process so that the center is removed equally from each side. HOWEVER, this can only be done if you can stand the board up on its 'ears' and all ears touch the surface of a table saw. If they don't, this cut becomes dangerous because you can slightly change the direction of the wood as it passes the saw blade and that could cause binding. If the ears don't all touch, you can double-side tape a board on top of the generation board that extends beyond the ears and use that board against the fence. It is a far better idea, though, to make sure that the generation board is made correctly so that it can be used as first described.
I then turn the two halves around so that the sawtooth is now away from the fence and make all remaining cuts in that orientation.
As for cutting the thin strips, I always calibrate my fence before each project so that I can rely on the the fence's gauge. If it is 1/8" or more, I use the GRRipper with an 1/8" attachment and I always use a sacrificial block on the end so that it is positively carried through the cut with pressure from both the top and the rear.
I love that the GRRipper lets me carry the wood on both sides of the blade completely through the cut.
Lloyd