Employing nucleases is a good idea. Instead of sonication, you can try using syringe with needle. Since the nuclear extracts are normally in high concentration, you can also try diluting it which might help in reducing the viscosity. Yet, in sensitive techniques like EMSA, it is always better to use extraction kits (I used NE-PER kit from Thermo and it worked fantastically). You could avoid cytoplasmic protein contamination too.
while running the gel, it is mentioned in EMSA kit (from thermofisher 20148 ) that we need to electrophorese samples until the bromophenol blue dye has migrated approximately 2/3 to 3/4 down the length of the gel. Do you follow the same for the nuclear extract ? because I feel that the bands are trapped in the upper part of the gel, and I only can detect cytoplasmic extract bands not nuclear extract.