It's difficult but not impossible to thoroughly bleed a master cylinder on the car. When you think you have it bled, go through the bleed procedure again.
Not sure why you would need to remove the front calipers to bleed them. Have you considered using a vacuum pump to bleed the system? It pulls the fluid, and air, through the system. Brake bleed vacuum pumps are relatively cheap and make the job easier, especially if you're doing it by yourself.
Definitely check your pushrod clearance as that can cause problems if out of spec.