Filling gap between Schluter transition strip and drywall
I just did something similar to your option 3. I used setting compound (Durabond 90) to fill the gap and smooth out it as best as a could.

After I got it pretty level I used a layer of paper tape to create a smooth surface, and finished with a small amount of premixed finishing compound then texture in my case.
You can use the Schluter as kind of screed surface after you cover with blue tape. I changed it between each layer to keep the build up of compound minimal.

Since drywall near water is always susceptible I did 2 coats of primer Zins BIN 123

Then 2 coats of a satin

I'll caulk the transition with a thin bead of clear silicone once I finish the floor. If you look closely you can see the wall bends in behind to the Schluter because its not flat but its not as noticeable from far away when finished.