I've had similar problems with my Jag/RF switch for years. The RF box that came with the unit produces a vertical bar of static along the left edge of the screen about 1 inch wide. It gets wider when I use it with my JagCD unit.
To solve the problem I just swapped my NES and Jag RF boxes. Each works fine in the other's system, and the NES one seems to remove most of the static from the Jag's performance.