For overlapping peaks there isn't much that can be done to get an accurate integration because overlap causes the number to skew. I would just go from the cosy to see how many of the target protons are under a peak. Watch out for water because it will change the chemical shift (ternary mixtures). Water can be removed using an azeotrope. If the molecule is fragile, then cyclohexane (mixture boils ~60°C). Benzene, toluene, MeCN etc. will work. To get the best results, I would recrystallize. The final thing that can be done is to use an instrument with a larger magnet to get the peaks to separate more, and to use a different solvent than CDCl3. The larger the diamagnetic current of the solvent, the more peak separation will be seen. CDCl3<DMSO<acetone<nitromethane. The samller π to π* gap the better.