I also have an Eastman fiberglass case, and I'm very fond of it, though I feel it could use a little more space. However, now that I'm mostly carrying an A style mandolin in it, I find I do have a little extra space where the scroll of my F style would have been. Even so though, with some creativity I did manage to fit in (with an F style in there) a tuner, my pouch of picks, a spare set of strings, a humidifier, and a strap, still attached.
Another option is to get a little pouch made for a point and shoot digital camera, and attach it to the case shoulder strap (assuming you use one, I do but not the stock one) using the little belt loop on the back side of the pouch. I have done this in the past, and it nicely provides some more space for small tools, string winder, tuner battery, etc., things that don't necessarily need to be in the case, but are nice to have with it.
"Aerodynamically the bumblebee shouldn’t be able to fly, but the bumblebee doesn’t know that so it goes on flying anyway."
Newell A5 #37, Glenn F5 #66, Eastman 615 #537,