Just a minor nitpick, but adding a GNU license to the code base do not mean you have to change the license. The distribution of a code base that combines different licenses must simply follow each and every condition of the compatible licenses.

The effective license will of course look very similar to the GNU license, since following the GNU license conditions will most of the time also mean that you are in compliance with the permissive licenses conditions, but there are exceptions. For example, GPLv3 do not forbid distributors to use the authors names in the promotion of products, but it is compatible (under the additional terms section) with 3-clause BSD that explicitly do forbid such promotion.