Keep in mind that even with a larger gauge, a B will usually have lower tension than the G it's replacing in a BEAD setup. For example, using D'addario's tension figures for a 45-130 XL nickel wound long scale set, the 130 B has 34.5 lbs. tension, while the 045 G has 42.8 lbs. tension. And in the 40-125 set, the 125 B is 31.4 lbs., the 040 G is 33.7 lbs.
So going BEAD isn't likely to put more tension on the neck. In some cases you may have to loosen the truss rod.