Without cleanup that’s just not possible. It will create concave ngons that don’t bevel well, or do anything else well for that matter.
Convert just the base letter, without extrusion or bevel. After converting, limited dissolve it and remove doubles (increase merge distance a little bit), then cut it up into convex ngons. Add a Solidify and Bevel modifiers, clean up the remaining areas where there’s still overlap. Setting Outer Miter to Arc in Bevel modifier might help.
However, when you do do the cutout, you’ll get the same problem on the cube, and will need to clean that up as well.