This is not a duplicate of Ender 3 first print some area is smooth but some is rough? -- that question has vertical, curved surfaces that are rough. My vertical, curved surfaces are fine; it is horizontal flat surfaces that are rough.
Second, I apologize for the dust on the prints in the video. I've been trying approaches on this for a week and dust has collected since that time.
I have an Ender 3 Neo and am using 1.75 mm Comgrow PLA filament. I'm using Cura as my slicer.
My problem is that all of my prints are fine, except some (the larger) horizontally flat sections print sandpapery to the touch. The walls are fine and smooth. Curved sections (such as a rabbit) are fine and smooth -- it is only horizontal surfaces that have this problem, and then only the larger ones.
By rough, I mean there are visually distinctive diagonal lines (which are on all my prints, smooth or not, so I assume are normal), but dragging my finger over them is like dragging it over fine-grained sandpaper. 
My tests consisted mostly of Incarna Tokens.stl -- this is the picture above. It's a mostly rectangular container to hold pieces for a board game, with a flat bottom that prints rough and walls.
What I've Tried:
Original prints were with the default settings for the "Creality Ender-3 / Ender 3-v2" at Cura's super quality (0.12 mm) and had the problem.
Releveling the bed. I did this several times, using this Creality Service tutorial video: lower nozzle to 0 mm, adjust Z-offset until I could feel it rub against the nozzle but could still push and pull the paper in any direction. I then turned off the motor and manually moved the extruder to each corner, where I repeated it while turning the corner dials to raise/lower that corner. Things actually got worse.
I then tried the method again, but instead of turning off the motor, I used the motor to move the extruder to each corner. I got different results for the corners, which I don't understand. But adjusting using this method got prints going fine again... except for the horizontal sections which were still rough.
I tried adjusting the Z-offset and reprinting just on the center (not adjusting the corners) up by 0.05 mm and 0.1 mm, which only succeeded in making the prints stringier, and down by -0.05 mm and -0.1 mm, which just made them worse. I took this as evidence that my leveling with the paper was correct (enough).
I tried printing at each of the corners. No change, all prints came out the same.
I removed the filament and cleaned the nozzle with the needle provided with the printer. The pin came out with some tiny black specks but nothing that said "clog." Prints afterward were no different.
I adjust settings in Cura. Based on various things I read, I lowered print speed from 50 mm/s to 40 mm/s, I changed the flow to 97 % and then 95 %, I changed line width from 0.4 mm to 0.3 mm, I changed bed temperature from 50 °F to 60 °F (nozzle temperature stayed at 200 °F), I lowered fan speed from 100 % to 50 %, and I did combinations of these things. None of these had a noticeable impact other than the print speed and line width making it take longer.
I turned on ironing in Cura. This worked, but only sort of: 2/3 of the horizontal surface did not have diagonal lines and was completely smooth, a strip around the edges (the ironing offset) had diagonal lines but was still smooth, but 1/3 of the print still had diagonal lines and remains rough.
If the ironing completely worked it would solve my problem (I don't care about diagonal lines at the edges), but it only seems to be a 2/3 solution or so.I adjusted ironing settings (following some page that I can't find anymore). I turned on monotonic ironing order, increased the line spacing from 0.1 mm to 0.2 mm, increased ironing flow from 10 % to 15 %, and increased ironing speed from 16.66 mm/s to 30 mm/s, then 50 mm/s, then 70 mm/s. None of these solved the problem that about a third of the print remained rough.
I measured the prints for X/Y dimensional accuracy. I don't have calipers or a precise tool, just a ruler and my eyeball, but they seemed fine. I also printed xyzCalibration_cube.stl -- a 20 mm cube -- to test the Z accuracy, which to my eyeball, is also fine. Vexingly, even back to entirely default settings / 0.12 mm print speed, the calibration cube is smooth on all sides, including the horizontal top, which still has the diagonal lines but feels smooth to the touch like I want.
I printed some other prints. The default rabbit print the Ender comes with (no horizontal flat surface, just curved surfaces) prints fine. Small horizontal surfaces (the cube, all of these Gloomhaven standee prints) print fine -- diagonal lines but smooth to the touch. Larger horizontal surfaces (like Dahan_Tray_thin.stl) continue to print rough.
I checked the large surfaces to see if they start smooth in a corner and then get rough, but no, the roughness is consistent across the entire surface.
I theorize, but do not have any experience to back it up, that this happens because the larger flat area means more elapsed time between layers, but even if that's true I don't know how I would counteract it. Looking at the closeup pictures, it seems like the line ridges are raised, but then why doesn't it happen on smaller prints?
So I turn to you. How do I stop my large horizontal prints from being sandpapery?
