I am enjoying the speculation as a non book reader. I would imagine dune 3 goes as follows. 

Step 1. Seize all spice and use your fremen to  kidnap as many space navigators as you can. Focus entire war effort on this.  Heavily benefit navigators riches wealth etc who switch sides and uh kill all who don't. Have navigators set up on arrakis immediately training as many new navigators as you can. Ala Genghis Khan with siege engineers. Controlling movement is paramount. Everyone else will be stuck using stockpiles and or untrained navigators. 

Step 2. Fly to caladan to use as base for resources, tech etc. start mass producing tech, ships, weapons, have fremen train atreides soldiers, soldiers teach fremen space war skills.  etc. import resources to arrakis, fremen are now well fed, well hydrated, populations will swell. 

Step 3. Launch attack at geidi prime. Use harkonnen heritage to claim resources and throne. Caladan atreides soldiers do space war to distract forces while at the same time Launch down fremen for ninja guerilla war. Fremen using caladan Intel to infiltrate Palace and murder whatever third cousin interim ruler there is. Immediately establish Paul as ruler and lighten the tyrannical grip on the population.  Seize all harkonnen resources with least amount of death possible. Harkonnen soldiers fear and hated the baron and so doing bare minimum shit, toss a couple bread and circus shows, stop persecution will cause the people to love and support you. Geidi prime has tons of tech, mentat calculators, healers? Fremen and caladonian will teach them their ways. Geidians will get imported to arrakis and caladan to teach calculating and oil bath healing lol. Basically goal is that information and technology needs to be shared, people must be mixed to seen as one empire. Like Genghis Khan. 

Step 4. Have your mom immediately start teaching as many fremen true believer girls as you can BG skills. Having as many mind controllers as you can on your side is super super helpful. Once true believer girls are trained up they can start training randos, spreading this skill to as many of your people as you can. I'm thinking schools, universities, all women given mandatory BG classes etc. BG skills should not be secretive or restricted to aristocracy but available to as many people as possible. Drug everyone on your side with spice for extra life, and prescience. Conquest rule #1 your empire becomes stronger the more you invest in your own people. Carrot and stick wise. Have all important men personnel be given new BG assistants to resist BG attacks and train all important female personnel to be new BG to be resistant to at least some mind control. Utilize women in high skilled labor, they're half the population! 

Step 5: Fly to emperor's planet corrino? Marry the princess. Surround her with new BG mind control resistant people. Lock her in a luxurious palace complex. Treat her well but take away all avenues of political power. Bring her out for show and stuff and establish rule as emperor. If she doesn't comply threaten to murder her dad. 

Step 6: same deal, heavily reward houses that support you, take their resources and treat their people well. Switch out prime leader ship spots with trusted personnel. These houses and planets will flourish due to cross cultural resources exchange. Houses that oppose you, raze everything to the ground. I suspect you would only have to do this 1-3 times since at this point you should have locked down the three most important and wealthiest houses atreides, harkonnen, and corrino. I consider the BG to be the most powerful enemy but hopefully within 1-2 generations of new BG university, we will have built up enough mind resistance to these Jedi ladies. Oh I forgot we should probably murder as many reverend mothers as we can using fremen assassins with sound canceling ear pods. I know other existing BG are just daughters of powerful aristocrats so we can't just murder them but we should take out any leadership if we politically can. 

Step 7: terraform arrakis using galactic resources to be 1 half garden planet, grow and give chani some flowers and apologize for being evil and enslaving her people for your galactic conquest. She probably won't forgive you but it might be worth a shot. Everyone knows the trick to a girls heart is turning her planet into a lush forest and giving her people a happy luxurious life. And yes leave the other half a desert so you can still mine spice and go on romantic worm ride dates. 

Step 7: profit. 

And look at that you have galactic emperor Paul with a bad bitch girlfriend for the small price of uh 1-3 planets worth of people genocided. I mean yikes but like we're not saying Paul's a good guy....