Dave - You are correct. The instructions for the core support installation don't specify either way about the K Member, but I have to believe it's a good idea to keep things lined up when welding.
All of my front suspension is out, and this information was included in my question asked of Chris at US Cartool. As for the inner fender braces, mine were installed at the body shop where it was painted. The wheels were on, engine and tranny in. This is from the US Cartool installation instructions for the inner fender braces:
"At this point you want to correctly support you car for welding. If your car is completely disassembled, you will want to support on jack stands under the frame rails of the car in multiple spots. If the car is on a rotisserie you will need to lower it down and support with jack stands. You do not want to weld these in place with the car supported only by the rotisserie. If your car is completely assembled you can install these with the car sitting on all four wheels as it would be normally. These steps will insure that the body does not flex while installing the inner fender braces."
There was also a comment in the instructions about removing the front shocks before welding, mostly to keep the shocks from being damaged by weld splatter.
Link to the full set of instructions for the inner fender braces:
http://uscartool.com/wp-content/uploads/2014/11/Inner-fender-Brace-instructions.pdfLink to a list of all of the installation instructions for US Cartool products:
http://uscartool.com/picturesUp to this point, I didn't have any plans for adding the core support brace. Now I'm thinking about it. The subframe connectors and inner fender braces will be there along with the torque boxes, the K member stiffening kit has been installed, plus I'll be adding one of the sector support bearings for the steering. The concern is leaving a "weak link" in place at the core support with everything else being reinforced.
I promised myself that I'm not going to go buy more parts (at least any major ones) until I work down the pile that are sitting in my garage and basement, so a final call on the core support brace will have to wait until I'm closer to reuniting the engine and the car. As has been said many times on this board, our project cars are never "done."