Re: Convert to Islam or die!
The problem is that you cannot say that EVERYONE was converted by sword. A vast majority was actually not. Much conversion was done through initial missionary work.
Once people were receptive and open, the empire came in. Of course, you cite examples that might be true, but that doesn't mean the entire Islamic empire was won over that way.
Even to this day, conversions take place, and none of it is being done militarily.
Missionary work? Umayyads (possibly following some sort of example) did not encourage conversion (not at least till Umar bin Abdul Aziz) since they benefitted from the jizyah from their dhimmi subjects... many people converted for sake of avoiding the toll. "Missionary" work as you see it, began, or was revived (though I am careful in using this term for a certain reason), in Abbasid times...