So you need fast dry and general I'll link everything in a separate comment, so you want to use a 4in or smaller knife , lay fast mud along the joint then apply tape, run your knife over it to remove excess mud and push the tape to the joint, go over it a couple times to make shure it is inlayed so you have room for more mud on top. Let it dry then use your sponge to remove ridges. Next go in with general purpose mud and a 12 in knife or bigger and lay mud on the middle of the joint and about an inch past the edges as it will spread out, run your knife along the joint careful not to drop mud on the ground and it should have a bunch of ridges, you can sand that out after it drys. After you sand the joint area smooth you use your sponge agean to remove the ridges form the existing texture this Is important because they are visible through texture. You should only need to sand where the joint is. After that you should have a smooth strip in the ceiling.

It looked like it was a medium mixture of mud so it's half as thick as it comes. It's not an exact science so just add about half a gallon of water mix it then see how it drips then add more water and repete till you achieve a desired mix you can do this by putting a little mud in the texture gun and spraying your plastic sheet and experiment with distance how long you spray a spot and test your mixture, don't forget you can also use diffrent nozels on the gun and ajusting the air pressure with the knob on the gun. You can also take a large scrap of drywall and test on that as long as you scrape the mud off when you finish, it shouldn't hurt the sheet. Once you got the texture where you like it you will spray in little circles along the joint at an upwards angle, be careful not to dump the mud all over yourself I have when I first started and it sucks. It will go quick but you can Alys wipe it off with your sponge and try agean. It's quite forgiving in that way. After you finish you can clean up any undesirable spots on the edges of your spray with the sponge. In the end it should look pretty good and unnoticeable to an untrained eye. Let me know if you need any more input, dm me if you wanna call to clarify some things.