First - yes you do have a problem with the lug spacing on the CJ - the information I have is that it is 5 x 5.5 meaning the center of the lugs is a 5 1/2" circle. The JK at 5 x 5 is at least closer than the YJ/TJ which is 5 x 4.5.
Second - the CJ and most vehicles of that era had negative offset, meaning that the mounting surface of the wheel was closer to the inside of the wheel than to the outside of the wheel. The YJ and all subsequent Wranglers have positive offset which means that the mounting surface of the wheel is closer to the outside (road side) of the wheel than to the inside.
If you mount the adapter to your hubs and then put the CJ wheels on they will really stick out. From the outside the outer surface of a negative offset wheel looks almost flush with the outside rim - YJ/TJ/JK all look like this. The CJ with it's negative offset had a deep inset look to the center of the wheel.
This came about for a good reason, in designing the YJ, Jeep wanted to increase the stability of the Wrangler over the CJ (they were getting hammered over the "rollover problem" in the press), so they lowered the vehicle and widened the frame which required longer axles. To avoid the wheels sticking so far out, they changed to negative offset wheel which at that point were most commonly found on front wheel drive cars. This gave room for the hubs to be further into the wheel. To keep people from mixing up the CJ/YJ wheels they changed the lug pattern as well. They reduced the diameter of the lug spacing circle which required reducing the center hole size and they as a result also eliminated the manual hubs.
Yes, you can mount the spacers and then you can mount the "deep dish" CJ wheels, but you will have wheels sticking further out (I would estimate at least 5" or more) and this will lengthen the moment arm of force on the wheel bearings. The result will be adverse wear on the bearings and you could upset the suspension settings and that in turn will affect how it turns and how it behaves.
This is the long answer instead of the short - "it's a bad idea". Your best bet is to go with wheels specifically designed for the JK. If you are going oversized tires that may rub, a small spacer can be used but it will only cause a small adverse force.
Stock CJ wheels of the CJ-5 and CJ-7 era where basically a white spoke wheel, not very military looking. The original wheels on the MB were negative offset, but will not fit over the brake calipers. One reason for the bigger wheels on the JK is bigger brakes to stop a heavier vehicle.