The GPL is "viral" in that if you use even a smattering of GPLed code, you are required to release ALL of your code as GPL as well.
Not true. Go back and re-read the GPL. You are required to release your code under a license that places no more restrictions on it than the GPL. You must also license the combined work under the GPL. It is, however, completely fine to take a few files of GPL'd code, combine them with some BSDL'd code files (as long as those files are not a derived work of the GPL'd code) and ship the resulting program under the GPL. If someone else takes only the BSDL'd files for use in another project then they are not bound by the GPL.
There are two ways in which the GPL is 'viral'. The first is that you cannot change the license of something that you do not own, so any derived works retain the copyright and license of the original. The second is that the GPL is a distribution license and, if you wish to retain the right to distribute it, then you must not distribute it in a way that does not pass on the freedoms listed in the license (meaning that the combined work must grant all of the permissions as the GPL'd parts).