How did a Balrog get beneath Moria and when?

[Cirdan]

In Appendix A to the Lord of the Rings we are told that:

"It came to pass that in the middle of the Third Age Durin was again its king, being the sixth of that name. The Dwarves delved deep at that time, seeking beneath Barazinbar for mithril, the metal beyond price that was becoming yearly ever harder to win. Thus they roused from sleep a thing of terror that, flying from Thangorodrim, had lain hidden at the foundations of the earth since the coming of the Host of the West: a Balrog of Morgoth."

This would seem to refer to the War of Wrath that broke Thangorodrim and that occurred well after the establishment of Khazad-dum by Durin I, and yet, a "host from the West" assaulted Morgoth's fortresses (including Angband) long ages before (just after the Elves awoke) in the War of the Powers. Of that this was written:

"Nonetheless the Valar did not discover all the mighty vaults and caverns hidden with deceit far under the fortresses of Angband and Utumno. Many evil things still lingered there, and others were dispersed and fled into the dark and roamed into the waste places of the world awaiting a more evil hour..."

Could it be possible that this Balrog was a refugee from that conflict, taking flight and hiding under the Misty Mountains before even the Dwarves founded Moria?

If not and this Balrog is indeed from the War of Wrath, then just how did it sneak in under the Dwarves' noses, why did it go to sleep if there were Dwarves nearby to slay and terrorize, and how did it remain hidden there for almost 5500 years?

Any thoughts?