Q)If I added more sugar and yeast will that give it a higher ABV?
A)Yes, but you don't have to pitch more yeast.
Q)Should I bother with the 2nd round of sugar and champagne yeast or just strain,add sugar and bottle?
A)Your choice, add more sugar to increase ABV.
If you haven't read Pappers sticky on stovetop pasteurizing, it's time. It will tell you all you need to know about bottle carbing.