FSI Wichita / Kansas can give you a JAA CR for the CJ series. I did it myself in 2002 there. Have a look at their homepage.
I donīt how restricting the TSA bull**** is for the CJ, but I wonīt go back into the US for training if I can avoid it. Their paranoia is disgusting. All the while the europeans will give them insight into swift account transactions if the legislation (most like it will) passes next monday.
BTT, if you fly the CJ as your first jet class rating with little experience, it will fly away from you anyhow. The sim gives you all the time you need to discuss what happens because the trainer can freeze it. The learning curve is steeper.
I did my CJ2 rating on the airplane, because no sim slot was available and went to the sim 4 months later (I had a 500/550/560 rating and experience before).
I learned way more in the sim than on the airplane.