I gave it much though, and I think any W40k mod for Stellaris must take two important issues into consideration.
Completely different value systems in both universes. Optimism vs Pessimism
Stellaris is a game centered on stuff research, exploration. Progress, however you define it depending on your values. Game is ultimately optimistic, and all its mechanics are centered about it.
Warhammer40k is about war, despair, decay, trying to stave off the ultimately inevitable horrors. Pessimistic universe. There would have almost no research. Adeptum Mechanicus would occasionally uncover lost technology, but to improve existing design would be heresy. Same thing with most other factions. Technological stasis. That means major feature would be effectively cut from the game.
Secondarily, number of players. There would be less than 8 playable empires, unless one would successfully jury-rig federation system to play as subfactions.
So, here is my concept to reconcile W40k lore with Stellaris gameplay:
Imperium of Man and most of other Major Factions, like Eldar and Necron, would be unplayable a Fallen Empires. Large and powerful, but ultimately stagnant and doomed to eventual decay. Other Factions like Tyranids and most of Orks and Chaos Marines would be randomly spawned marauding menaces (like space amoebas), but stronger, capable of depopulating planets after defeating their defenses.
Most playable civilisations would be lost Human colonies, far away from borders of the Imperium. Left on their own devices, they developed their own culture, technology and ethos system, though they would be under constant threat of Imperial Crusade.
Other than Humans, as far as playable races go, there could be slightly more civilised Ork warbands and slightly less crazy Chaos Cultist groups, which managed to organise enough to be actual full-fledged playable civilisations, offshoots of Eldar who actually started to rebuild their civilisation and colonise planets. Tau Empire could be playable as it was portrayed, but playable Tau offshots would make sense as well.
In other words, one would play as an offshoot of major factions, not major factions. Because almost all canonical major factions would be unplayable without completely butchering the lore.
Some of late-game threats would be: Awakening of God-Emperor, Arrival of main body of Tyranids, Awakening of Necron.