Couple of suggestions for you.
(1st) I would remove the entire "Plastic" corner strip and replace it with "Metal". I have used the plastic a couple times and ended up with the wavy look you mention. The plastic tends to bow out when drywall screws are installed. The main hardware store in our area has ceased to sell the plastic due to all the consumer complaints!
(2nd) Add 2 teaspoons of liquid diswasher soap to your joint compound per gallon... it is tough to mix in and you may need to mix in a larger container... but this will make the compound Much easier to spread and give you a Smoother surface.
Last thought... you mentioned screw pop outs... this is odd, you should not have any screw pop outs if the screws are set into the drywall at least a 1/16 of an inch. Be certain that the screws at set into the drywell well before starting any finishing. Take your time... when working on corners...just do one side at at time, let it dry, sand, then do the opposite corner.
Hope this helps and let us know how it turns out.
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