The paint ridges, being quite a bit harder than drywall mud, will still show up after sanding the skimcoat; they may be a lot less prominent, but will still be visible in a raking light.
I think you need better sandpaper and a sanding block. There really are superior papers that will make this task far less arduous. The 120 grit Norton paper that has a white finish and a red backing paper is your best bet.
You can also get random orbit paper that is made for feathering paint not sanding wood. Put away the belt sander.
For a ROS 100 grit will be perfect, but by hand I'd stick with 120.
A solid rubber quarter-sheet sanding block may be found useful, or wrap a half sheet around a 6" length of 1x2 pine.
Casey

Thanks Casey...yes, the ridges ARE very hard. Surprisingly so...I always thought latex paint was sort of rubbery. I have a quarter-sheet rubber block, I will try the sheets you mentioned on it...and just expect that there is no easy way out of this, and I'm going to have very muscular arms in a few days. Haha.

Will irregular 120-grit block sanding marks then show up through my new paint?

I could kick this guy in the shins for striping this 14x14 room. Argh!

You might try getting one of those carbide scrapers, annika s, one of the pull kind, probably 1.5" wide or so. Easier and less mess than sanding down those ridges. Try to figure out just the right amount of pressure to take off the ridge without gouging the surface too much.

You'll still have to do something to smooth it out afterwards, maybe hit it with that fine sandpaper at that point. Personally, I'd probably skim-coat instead, but it it a bit tricky for a beginner, so maybe sanding would be good enough. A good skim-coat would leave a more uniform surface than sanding the old paint, however.

If you want to try skim coating, I'd recommend the powder-type (mix with water) drywall mud. I think it's called E-Z sand. I prefer it because it drys faster and doesn't shrink as it drys. Use a 12" knife. It won't go on very thick, just because of the thin consistency of the material. If you don't like the finish, give it another coat when the first one sets up enough.

The best professional advice I ever got on finishing drywall is "it's all in the angle of the knife". It's not a simple as it sounds, but once you get the feel for holding the knife angle just right, getting a good finish is much easier.

Thanks for the tips, tryinbrian.

I ended up following Casey's advice before I read your reply. It went well. A small rubber block worked better than a drywall sander. It took 3 hours and I am happy with how the ridges have gone away. I'm going to spackle a few dimples, then prime the whole deal to prevent flashing...then 2 coats of nice flat paint should look really good.

Only problem with this method is...now my arms are temporarily paralyzed. Ha.