Breathing from the diaphragm is not about not filling your lungs with air. It's about using different muscles to do this.

I have been having Buteyko treatment for emphysema for some time now. Buteyko is mainly about learning to breathe properly, and interestingly enough it emphasises the same thing that I was taught as a boy soprano many years ago. Breathe from the diaphragm. Place your hand on your stomach, feel the movement there as you breathe in and out rather than your shoulders and upper chest. It's a discipline that I had to relearn, and takes practice. Practice whenever you have a spare moment. Sit down, relax your shoulders, put your hands on your knees, look ahead and slightly down (relaxes the upper airways). Breathe in...feel your stomach push out, pause...breathe out by pushing your stomach in.   

Buteyko also emphasises breathing through the nose, not the mouth. This is not practical while singing, but certainly very valuable at other times. I get far fewer colds than I used to and to that extent the quality of my voice has improved. I still sing, but I find that lack of breath (I have about 35% lung function left) has restricted my range somewhat, and I have to rehearse songs from the point of view of learning to phrase them, and deciding where I will take breaths (something that I never had to think about before). You may find that doing this will also help your ability to project.