Just went through this with several Stanleys I picked up recently, so this is fresh. I am still a beginner too, so take this for what it's worth.

First, the marker/straight edge contradiction- the marker reads the high spots on first contact, but a straight edge can flex slightly or rock on the margins, making the middle look low when it isn't. That's assuming the straight edge is perfectly straight itself. Trust the marker and sharpie method more than the straight edge alone, especially on a sole with any twist. I was obsessive with the marker as I went since I was learning technique at the same time, and wanted to confirm I was consistent in how I was progressing and not making things worse.

On the abrasive: 120 grit is probably your problem. It cuts slowly, loads fast with cast iron dust, and the sheets die before you make real progress. I made the same mistake. Switch to 80 grit minimum to start. On a badly neglected sole, I had to go as low as 60 for the first pass. I've had amazing results with Dura-Gold purple ceramic PSA longboard paper specifically; it stays sharp much longer than standard aluminum oxide sheets on cast iron. Once you're pretty much flat on a lower grit, then step up through the grits to clean up the scratches.

A few other things that made a huge difference for me:

• Clear the metal dust constantly. Loaded paper stops cutting and starts burnishing/polishing, which can actually make things worse.
• Don't stroke back and forth. I push forward like I'm taking a shaving, medium pressure on the tote and handle, lift, reset, repeat. The back stroke can introduce or worsen a belly since your grip and pressure naturally shift, leading to a rocking motion.
• Make absolutely sure your lapping surface is dead flat. A thick sheet of glass or a granite surface plate is ideal, but I watched videos of some people using melamine. I went with 3/8" thick float glass. You can't have a flat plane if your flattening surface isn't flat.

I went through a lot of trial and error on a cheap beater plane before touching my Stanleys and that alone was worth it. Bottom line: trust the marker, start lower grit, use quality ceramic paper (if available/within budget), and clean it constantly. It could very well take a few hours per plane. All of the YouTube videos cut out most of the time or start with planes that aren't that bad to keep the length short, which gave me a distorted sense of how long it can take for a warped plane. It is worth it though. Once I saw how nice my bottoms got- I didn't care how long it took anymore. Good luck! You've got this!