Chris,
Your predicament sounds familiar to me. I use a modular system made by Rayco (800)847 6045. It has been a good setup for me and has saved me a lot of hours in the toolroom.
Somtetimes if I know that a part will be in production for a while, I will design and build a dedicated fixture to save setup time and to provide better consistancy. I usually lay out a plate of aluminum(cast tooling plate), place the part on it and envision the part in both positions required for probing. Then I look for a common edge or hole that will allow me to clock and stop the part in either position. Sometimes ,If the part is not to deep I will build a box or mill out a pocket and use Devcon Flexane, a 2 part goop that dries to a stable hard rubber like texture. You can make a very accurate impression of one side of the part. Wax the part or silicone it first or you'll never get it out. The finished casting can be machined nicely, if necessary. Usually the casting holds the part securely enough that clamping is not necessary. On some parts I have been able to put a couple dowel pins at one edge of the part so that it can be flipped and the other side presented to the probe. When in this position some light duty adjustable toggle clamps are usually required. You end up with a fixture that will hold the part in two positions from a common edge. Feel free to contact me at (505) 858 8761 (New Mexico, USA). I could email you some photos. Good Luck. Mike Canant