Help Residence Card Application (Birmingham)

I recently moved to uk from Germany on EEA family permit visa. My husband is a German national and i am a Pakistani national. I have a 6 months visa for uk till August Protected content . Husband is a permanent employee here. I want to apply for the residence card. But i read that the process takes minimum 6 months that too if u r lucky and meanwhile the embassy will keep all the original documents with them including passport. Considering i need to travel to Germany in the month of May, then back to Uk in June and to Pakistan in December what should i do?? Should i not apply for the residence card before Protected content ?? If I apply i wil be stucked in the uk and can't move elsewhere keeping in mind that my original passport will be with the embassy. What should i do?? Is there any other way that i can both apply for the residence card and travel easily to Pakistan n Germany.???

Please Help#
Thanks in advance