Removing a wallpaper border which has been painted over
I had a similar issue and though it sounds like a lot of work and hard for a diy'er to do ( *I found a lot of sites that simply said call in a professional. ) 
However,  for me that just wasn't an option due to finances. I too am told by many that I am too much of a perfectionist agree. I will say it has both advantages and disadvantages. Give yourself credit and confidence first. 

There are a few ways to handle this in my personal experience, I will share first the one I think has the nicest outcome. Which is...brace yourself and have an open mind, YOU CAN DO THIS!  ( "this" is re-skimming the wall. )  

Ok make a list of the NEEDS to do then head on down to your local home improvement store to purchase needed supplies. These supplies will be in two categories, 1st is tools. Tools do make all the difference in the outcome of the task at hand. You don't have to trust me, but if you don't you will soon learn! 

Needs: 

A dry wall taping knife, at LEAST a 10," I used a 14"  ( do to me being a 5' 100 lb 50+ girl in hind sight a 12" would have been easier for me I think ).

Drywall mud pan/tray, one that is the size of the knife you choose. 

A pole sanding tool, ( looks close to a swifer floor duster ) That's optional, their are many ways and tools to sand the wall. I used the pole sander and also a 3' pc of 1x4 smooth board. I did try my electric palm sander for about 2 mins lol, it made sooooo much dust fly everywhere!! Again remember Im a diy'er and will NOT be doing this for anyone just in my own home. So with that it said I found it too costly to purchase anything more than this pole sanding tool.

Drywall sanding paper, (looks like a screen) to fit your pole. not real sure what grit it was tiny little squares a tad smaller than what graph paper look like. I also got a pack of regular sand paper idk 8x10 like a sheet of paper I got grit of 220. (hence perfectionist)

Drywall Mud, MANY OPTIONS HERE! I tried a few and what I found to work best for me was the premixed white bucket with a blue lid. All purpose drywall "compound" the blue lid is "Plus  3"

Drywall sealer/primer, Again many options I choose the zinsser bulls eye 1 2 3  all purpose primer, water clean up. 

Paint, and the tools for painting, ( I won't go into this will save for another category lol )

That is all you need to skim wall. I did 10 walls in my parents house do to a dishwasher house flood that  insurance did not cover. :( errr ) The walls came out GREAT they even impressed ME! After painting one wall I was fortunate my father  went and bought a graco  airless paint sprayer, Not the litte handheld thing , well first he did but had to refill cup way to much to make it worth while in my opinon returned that and got the jamb up one that has a hose to go into a 5 gallon bucket,  yeah!! I will NEVER ROLLER and BRUSH AGAIN!! Ahhh I love good tools!

Ok. now you have all you need. Now just do IT! Gitt'er done! Time frame for me was I did one coat a day x 3 days !

Opps forgot one item sorry! I got a big mixing thing that went onto my drill to mix this the drywall mud up. I don't think I got the RIGHT type mine looked like a mixer beater, the caged in type it worked though. I gave it a little whip not a lot just a bit, so it was like a creamy smooth peanut butter or a thick heavy cake frosting. Now with mud in pan, knife in hand skim a light layer on the wall I did top to bottom, bottom to top. Scooted over to next path of which I over lapped a bit on each. Do this and wait for the next day and repeat ( no need to sand but you many want to run a putty knife to knock down any lines you created before you Repeat! Oh yeah on the repeat I went side to side meaning not up and down vertical, but horizontal ) 

Day 3.  Now on this coat I went vertical but I thinned down the "mud/compound" not too much just a little, made it creamier, I will say like tub type cool whip! This is the final coat so before I put it on I ran my knife and really looked to see areas where I may need to pay more attention to. I am a touchy/feely person and with my eyes closed I ran my hand all over the wall.  I could  feel waves &amp; dips and the like so I knew where and what I needed to do to get the smoothness I wanted. ok I put it on! 

Now day 4, sanding time! Put the screen on your pole and hit! NOT ALOT don't use to much pressure, let the tool do the work for you or you may just  have to give this ANOTHER coat, ( NOOOOOO hahah ! ) just run it up and down and then side to side. Now the wall is MOST LIKELY READY TO seal\prime . Well you have to get a damp cloth and I do mean EVER SO SLIGHTLY DAMP, like really not even but damp. This is to clean all the dust off the wall so that the primer/sealer will stick! Vacuum too, get all the dust outta there! 

But before the dusting, I have to be me, so I took the board I previously mentioned and I wrapped it in the 220 regular sand paper, held it on tight with a few staples on the back where I held it. I took this as a sanding straight edge and ran it up and down my corners and ceiling edge then I slid it all around the wall in every direction in circles too like an orbiting tool. Then I was pretty satisfied. 

I sealed and painted and WOW the walls look amazing..... They look better than ever, this even took out the slight hump that the original builders left at the seams! You too can do this I am positive. Just don't over work the mud, do it in layers. Each layer makes it better. No the walls, to ME, did not FEEL perfect when I sealed them either! I was gonna give them another layer of compound mud, but my father insisted enough! I was like well IF YOU SAY SO BUT....... Hind sight it is true here.... FATHER KNOWS BEST! 

The walls simply look GREAT and REALLY this is NOT HARD work JUST time and self confidence, leave negative thoughts somewhere far from you! You I am sure will gain another notch in self accomplishments.

Other options: re drywall, cover with any other kind of material, just try to fill in the strip with mud, get the texture in a can..... Im not for any of those really that's my personal opinion. 
You can create a whole new kind of texture with the mud/compound too many cool ideas out there, google it. 

My dads boy is a girl! hahaha cuz that's me! ... I want the world to know I sure love my daddyO! 
Hope this helps at least one.   Peace my friends :)