Before going through a lot of trouble, I recommend applying one more coat of primer then paint to see if the strip of texture is noticeable.
If it is, you could try a palm sander with heavier grit sandpaper (60 or 80 grit) to reduce the texture. Then, apply drywall mud to smooth out these areas. The drywall mud could turn out smoother than the surrounding areas after it is sanded. To remedy this problem mix a little drywall mud into some of your primer (latex or acrylic only) and roll it onto the new smooth surface. Use a 1/4 inch nap roller for a finer texture. This would help blend these areas into the surrounding wall.