Your description of the problem implies that there indeed is air in the line that needs to be bled out. At this point, the why of it all is somewhat moot.
The question I have is, why remove the calipers? I can use a front stand, or in a pinch, suspend the front-end from the rafters, and drop the front wheel out in the process sliding the rotors out from the calipers.
This way, no oopsies or dropsies!
I prefer a vacuum bleeder, but there are those who profess that pumping is better. Any way you choose, bleed those brakes and you might as well replace the fluid while you're there.
I plan to die young, as late as possible.