Mountains of Mordor

[Kuruharan]

Which maps? If you mean the maps in The Atlas of Middle Earth they were drawn by the author Karen Wynn Fonstad. Here's what she has to say about where she got her materials...

The maps detailing the lands of the earlier ages, especially those in volume four, The Shaping of Middle-earth, were especially helpful in remapping the whole of Arda.

About the Inland Sea of Helcar it says...

the Inland Sea of Helcar, formed by the meltwaters of the pillar of Illuin.

Reading all of this I found that I had forgotten another time when the Mountains of Mordor could have been raised, the Siege of Utumno. I suppose that it is possible that they could have been raised by Melkor during the tumalts, but they still would have been under the Sea of Helcar and as I said earlier it's hard to see how they could be of the least use there. I suppose they could have been there submerged, but I don't think that they would have been connected to the White Mountains, they would not have been on the same plate. (Although I must admit that my understanding of plate tectonics is small).
I think I'll still sticking to my Breaking of Thangorodrim theory.