I think I may have figured out why you guys are having problems with the cloak. I can confirm that the BSAA and the battlesuit Jill are not exactly 100% the same body. Whether they are the close but one is modified or it's an entirely new body, I don't know but it's not 100% the same tho. I went ahead and unboxed my BSAA that I have for sale just to check and the neck tilts down. It was bugging the crap out of me cause I knew her head was tilted down when I had the BSAA displayed.
The thing is, it's not just the head, but the neck itself is moveable so you can tilt it down. The battlesuit has a fixed seamless neck like wolverine or Royce body. I'm thinking maybe the battlesuit is a combo of black widow and BSAA Jill. Matbe the cloak was originally measured for the BSAA which may have a slimmer body so it is why the cloak is really tight on this battlesuit body.