Deep Ones will be immortal zerg-rushing cannibals that won't trade anything of value to you, set arbitrary restrictions on the number of fish you're able to harvest, and get offended if you offer them anything made by Elder Thing SCIENCE! On the other hand, Deep Ones would engage in kidnapping and interbreeding. They also worship Cthuloids that reside in Dark Cities. So, a combination of DF elves and DF goblins.
Cthuloids would be Demons with some heavy bonuses are worshipped by the Deep Ones. Dark Cities would be Dark Towers, there's no need to go all 5-D Space on this.
A Deep One siege would last a long goddamn time as they would keep reinforcing themselves and transporting siege equipment to the battlefield. This would work like trade caravans; "A group of Deep One heavy weapons has arrived from the North." Only they would stop outside the front of your fortress instead of inside the trading depot, and blow away squares of walls and stone. Projectiles that dig and move around on their own? Perhaps. WAR SHOGGOTHS.
Mi-Go would be like kobolds, only instead of taking wealth or food, they take limbs and parts of your Things. A Mi-Go raider would remove a brain, or a spine, or an arm, from the first Thing it can get the drop on.
Now, how would we work the Megabeasts, weapons, and Adventurers? Would the Adventurers be restricted to being human investigators looking around at these ancient sites of horror, or would we get to play as a Mi-Go warrior harvesting the brains of interesting specimens and putting them in jars in exchange for money and upgrades when we return to Yuggoth bases?
(Night Gaunts are, of course, Batmen and Birdmen and all other flying men. Byakhees are giant eagles. Giant Scorpions are rogue shoggoths).