Wow! Where did you hear all of this mis-information? Some other detailing discussion forum? Just goes to show how fast bad information travels and how easy it is for people to repeat information without ever verifying whether or not it's accurate.
Be that as it may... let me help you.
Removing sanding marks, even #3000 grit sanding marks is difficult in most cases because in most cases the paint is really hard, thus it will be very difficult your you and your four fingers to rub an applicator with some chemical long enough and hard enough and with the right action to actually remove the sanding marks and restore a scratch-free surface.
The good news is, it can be done. If you're lucky, your car's paint won't be as hard as glass, this will help you to work out defects by hand or with a dual action polisher.
Forget those other products you mentioned, whoever recommended them to you needs to start reading posts over here instead of where they're hanging out on.
The product you want is ScratchX.
Hopefully you haven't already sanded a hundred spots on your car! If you haven't, then try this, take your #3000 grit sanding paper and sand a small inconspicuous area that has the same paint the areas you want to repair have.
Then, try to remove your sanding marks in this inconspicuous area with ScratchX, apply a quarter size drop on to your foam applicator pad and then apply in a back and forth motion across the direction of the sanding marks with passion, rub for 2-3 minutes. You want to rub till the ScratchX looks oily somewhat like Vaseline would look if you were rubbing it on your finish, but don't rub so long that it's gone.
Now wipe off the residue and inspect. Are your sanding marks still there? If so, repeat the process.
Do this up to three times. If after the third time the sanding marks are gone, then you know you can remove your sanding marks and now you can decide if this is something you want to pursue to each of the areas you want to fix.
If the sanding marks are still present, then this tells you either your paint is very hard or your technique is not adequate or both and be thankful you did this in an inconspicuous area.
Besides removing your sanding marks, typically when you do this kind of finessing, if your touch up paint doesn't dry to a real hard state, then all this rubbing on top of it and on the clear coat around it will tend to remove much of the touch up paint, especially if you start to generate some heat.
Been there done that.
Like I say, it can be done, but it tends to be a lot more work than most people ever imagine.
We get these questions every Saturday at our Detailing 101 class and we try to put the focus back on the big picture, which is making the entire car look great, not a little spot the size of a flea, give or take a flea or two.
Noble pursuit, don't want to discourage, you, but do test your choice of product and your process first in an inconspicuous area before attempting to do the the same process where everyone's attention will be focused.
Best of luck...
Using a foam applicator pad, apply some