Looking good for Rhûn! Here's a wildcard, should you ever want to capture the "all races fought on both sides but Elves" line about Dagorlad (and Orcish mercenaries avaliable for everyone close to the Dead Marshes to cover that gap?):
Fallen Dwarf miniatures, by Anvil Industry + Preview
Some quite neat Lotrish miniatures, designed with Tolkien's setting and Weta Workshop's treatment of it in mind. Some Fallen Dwarves available for Rhûn, or at the very least eastern/exotic dwarves would fill the Dagorlad quota. Consider it:
4/7 great Dwarf tribes emigrated eastwards to the Orocarni mountain range, and given Sauron's influence over the eastern lands, they would at the very least be familiar with his agents. Their kings probably also received some of the seven rings to the Dwarf lords in their halls of stone. Since all races participated at both sides at Dagorlad, a logical step would be to assume that some far eastern Dwarves showed up on Sauron's side, whether as vassals, fanatics or mercenaries.
One way to implement them would be as highly expensive mercenaries available in one or two of the easternmost regions of Rhûn, another to provide a special fallen dwarf barrack (excessively expensive to represent the supposed rarity of such troops in Sauron's host and the logistical difficulties in marching all that way west with large regiments) in some key city, perhaps close by that mountain range on the southwestern shore of Lake Rhûn. A new model file or two would of course be welcome, but easiest would be to reskin a couple of existing dwarven model files a tad to suit the Easterling look better. Bronze armour scales, red and black cloth/leather, perhaps?
Finally, we know full well that these distant eastern dwarves were in some touch with western Middle-Earth. In the late third age, all seven Dwarf tribes sent armed forces to cleanse out the Misty Mountains in the brutal subterranean war between Dwarves and Orcs. Running with the more greyscale theme common for Tolkien's Dwarves in any Age, these exotic Dwarves wouldn't necessarily be evil, but could well have double loyalties to kin and Mordor liege in some cases. Having them as mercenaries in easternmost Rhûn would allow conquering Dwarf players to access their distant cousins and recruit them to the western cause instead of Sauron.
Also, would it be silly to make the starting territory of Rhûn smaller and more scattered? By the time of the Last Alliance, Sauron was quite fresh back in Mordor, and his hold on the southern and eastern lands might have become less than stone-stable in his absence when corrupting Númenor. To make the disparate tribes of the Easterlings, and mayhap also the Haradrim, appear as less a monolithic power bloc (even as a tribal confederacy) completely in the thrall of Sauron, how about letting the good Melkor-worshipping Mordor loyalists have to start their game with bloodshed as Khamûl and mortal human leaders bash heads together to unite the east? Then they can march on Gondor, and have troops already experienced and well accustomed to blood on their hometurf, as evident in the early gameplay.
One should always imagine the dynamics of the peripheral parts of the Middle-Earth map and beyond to be lively untold chapters, and part of achieving that would be for Rhûn/Khand and maybe even Harad/Umbar (though there you would have an inherited Black Númenorean colonial empire in place at the homeland's fall into the abyss) to have and fight some at home and build empire before striking west at the Dark Lord's behest.
Food for thought, ladies and gentlemen. Keep up the good work!