I don't think that a balrog could have ordered a dragon. Sauron, who was the mightiest of Melkor's servants, never tried it, which I think means he couldn't, or that it would have been very hard for him. If Sauron couldn't how could a balrog? Of course when Morgoth was still in Middle-Earth a balrog could have done that as Morgoth's lieteutenant, but not after the War of Wrath.
Besides, the balrogs never leave their bodies, or at least it isn't mentioned. I think this means they were sort of incarnated, like the istari, and therefore can be killed. I'm pretty much sure the fall from Zirak-Zigil was Durin's bane's last fall.
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"Out of doubt, out of dark to the day's rising I came singing in the sun, sword unsheathing. To hope's end I rode and to heart's breaking: Now for wrath, now for ruin and a red nightfall!"
~Eomer
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