Your squeegee sucks bro. Get you a 12" & pan, & go from there. Those rubbery things are for doing knockdown textures, they're not skim blades. I don't care what a soul on this earth has to say otherwise; whether it be any homebuilding show, website or forum, article, or dahgun'd sticker --- Ain't no skim tool. Ain't no arguing to it neither. Any argument anybody could try to have about it can prove only one thing-- Ain't no Finisher neither
Now goes to say: there's nothing wrong using a roller to apply the mud, it's all about how you roll it, use what's known as a "loop" roller when you do. It carries mud the best, and it washes out. Home Depit sells them in the paint department. On ceilings -- start out far away & just calmy roll the mud towards you, else you'll end up hunkin phat globs of mud off your roller skin into the floor; and pushing the roller away from you flings it in yer eyezzz..... and will make your state of mood, not a very good one. No sir.
Walls-- just start in the middle and push the mud up before coming top down with the roller. Best way to properly load an area with mud so that the coverage is enough to skim. I have done great work skimming by rolling the mud and wiping with a 42" & scraping back into the bucket with a 6", or even just a 14" knife & pan.... but using a spray rig & wiping with a big blade on a box handle is the ways of Jedi.