Hi,
I am a master student here at penn, and i am apply for my PhD this year too!
Basically, you can apply for BGS and BGG at the same time, it is doable! And labs here at penn is very collaborative. I have friends from both programs, they do rotation under different departments, which means you can reach out to PIs and do rotation in whichever lab you want, as long as you have a great talk with the PI during the rotation interview.
Hope it helps :)