This is just on the off chance that someone knows a pickup maker who will supply a partial pickup.
I want to have a separate pickup to amplify my 2 bass strings so that I can rout that signal into an octave divider to give me a bass. I already have an under saddle (Fishman Matrix) dealing with all the strings. This second pickup would be additional.
I did suggest that some bright maker actually manufactured a single unit that would give both the standard signal but would put the bottom 2 strings through a splitter. Hopefully someone will "invent" the beast.
i read about someone who uses a soundhole pickup with adjustable/removable pole pieces and only left in the bass string poles. another option might be one of the midi contraptions where each string can be modified electronically...
I have good and bad news...
Bad news first, there really isnt any practical way to make something work the way you want with your Fishman Matrix installed, however K&K Sound can make a custom undersaddle system that splits the undersaddle pickup with individual E/A- and D/G/B/E string pickups. It requires an external 2 channel preamp (that we make as well) and can easily be used the way you have described above.
If you are interested please contact Dieter or Jack at 1-800-867-6863.