I think that there are too many threads that would get tangled up by trying to intersect the movies too much.

I think the movies could be set up politically this way:
TFA - There is a cold war between The New Republic and a newly unified Imperial remnant known as the First Order. The Resistance is on a mission to find the last Jedi. The First Order launches a surprise attack on the New Republic.

TLJ - War rages across the galaxy, but things aren’t looking good for the crippled Republic. The Resistance struggles to survive as they try and hold out for Skywalker’s return, which is why Snoke lays siege to their forces in particular. Luke makes a heroic stand against the First Order and ignites a spark of hope throughout the galaxy.

TROS - Despite the First Order’s significant hold on the galaxy, the hope Luke inspired has ignited rebellions across their territory. Their resources are spread thin, and they’re desperate to find a solution. The new Supreme Leader, Kylo Ren, goes on a quest to find the source of his old master’s power.

The important thing, in my opinion, would be to find ways to foreshadow the existence of Palpatine in the previous two films. Maybe Vader’s helmet in Episode 7 could give Kylo a vision that hints toward Palpatine involvement. Things could be thrown into Rey’s vision as well.

When Snoke died, we could see the “blue flames” drift away from his body to imply a part of Palpatine’s spirit left it or was destroyed. This idea could also be applied to Vader’s helmet, and we could alter a scene in TROS to make it look like they accidentally destroy it and a “blue flame” dissipates from it as well.

I would also cut out any lines regarding a “Final Order” and let people assume the red troopers and other red dressed Imps are just First Order. I don’t think the implication should be there is a whole other Imperial remnant hiding deeper in the Unknown Regions, just the Sith Cult and the Emperor’s hidden Imperial armada.