4 mm difference between the old and new chiainrings? That sounds really high. Did you take the crank off to change them? Tighten the crank tighter than it was before when you put it back on?

Now the deed is done. You can add a spacer inside the fixed cup and move the whole BB out a bit. A few of us have brought life back to overly forced crank tapers using sheet aluminum (often from soda cans) between the spindle flats and the crank flats. There was a thread recently on doing this. Another option is a new BB with a longer spindle.

If you space out the outer ring; two cautions. You could have such a large gap between the chainrings that the chain falls into it and gets stuck. The end result could be bad. Also you want to make sure that the nut side of the chainring bolts has a sleeve long enough to project into the chainring. It is that sleeve that supports the chainring, not tension from the bolt. If the sleeve isn't long enough, the chairing will slip, the bolt and sleeve will elongate the holes in the spider and chainrings and you will end up needing to replace the crankset. (Not dangerous. Just expensive.)