The problem isn't just shaving, it's the case can swage the base of the bullet down. So be sure to pull your first few test rounds and put calipers on the base. Try a few different kinds of brass. If the base of the bullet is swaged to .354", then the entire exercise is fruitless. So you can flare deeper, but if you're using a short expander, it probably won't make any difference.
The Lee 38S&W expander, or a Lyman M die expander for 38, for instance, are much longer and expand the case where the bullet sits. But honestly, I think you need an even bigger plug ideally, for your bore. IMO you want a plug only about half a mil to a mil under your bullet size for cast bullets with 9mm or 40SW brass (which tends to be a little thicker and springier, compared to say 45ACP brass). Even a plug the same size as the bullet gives pretty darn good neck tension in most of these cases. And setback isn't even a concern. These rounds will look like a snake that swallowed a pig. I have to load my cast 9mm to -1 in some of my tighter doublestack mags.
The thinner brass like R-P, Speer, Blazer will yield to the oversize bullet better, in addition to possibly fitting in a tight chamber where other brass won't pass the plink test.
And load to the longest OAL that will work. The case often gets thicker the farther down you seat the bullet.
So getting a custom plug might be necessary. If the bullets fit, to begin with. You might even try an unsized case. Make sure it fits in the chamber. Flare it, seat a bullet, and then taper crimp a little to remove the flare. Then see if it even fits in the chamber.