Stochastic gradient descent in logistic regression
Stochastic gradient descent is a method of setting the parameters of the regressor; since the objective for logistic regression is convex (has only one maximum), this won't be an issue and SGD is generally only needed to improve convergence speed with masses of training data.

What your numbers suggest to me is that your features are not adequate to separate the classes. Consider adding extra features if you can think any any that are useful. You might also consider interactions and quadratic features in your original feature space.