your math is correct, but I think it is wrong to ignore high or low B/C grades.
Since prestige is a letter grade representation for a range of numeric values it is risky to assume that any C is exactly 1 letter grade below any B. When determining battle values, IMHO it is wise to assume you are the lowest possible whatever grade (C in this case) and your foe is the highest (B). If you are .01 ticks or whatever over the line of C/C- and your opponent is similarly close to B+ your real difference is much closer to 1 2/3 grades, meaning if you assumed you were safe with that 17k (for example) but really to equal his 10k you would need 21,600...
Also remember that A+ seems to have no upper limit, meaning that if you hit A+ at 97 of 100 or whatever it seems possible to go to well over 100 (or whatever the values are...) so A+ is even more volatile.
To your second question OP, you always have a shot, depending on circumstances. Most of the time you won't be able to take A schools, but at the C level its unlikely you'll be recruiting the same players unless said A got poached and is trolling for scraps...