Are you certain the grease gun head is attached fully to the lower nipples John such that you cannot pull gun off off nipple head when they are in line? (tilt and twist needed to remove). If not grease will just pour out of the sides of gun head.
It might be difficult with lowers due to nipple angle but beware of over tightening them to allow easier attachment angle as I believe they use a taper thread and are easy to shear off.