Why do I lose so much power/speed in an aggressive position?
I've heard many cyclist say they can go faster (and are more comfortable) with a large bar drop.


I think this initial assumption is somewhat faulty. Most riders will find they are less comfortable and can make less power in a forward, aggressive position. I certainly find that to be the case myself. (I'm a reasonably fit rider who can hang with the A group on local rides.)

You may just need to accept that your anatomy and strength just don't allow for a aggressive riding position. If you are riding in hilly terrain and are concerned with making your max power, set up your bars in a less aggressive position that is comfortable for you and just ride on the hoods. You can get in the drops on descents where max power output is less important compared to getting more aero.