Class II Division II with Moderate Crowding, Invisalign Can Correct A Deep Bite?

Your bite, from your description, is one that can benefit from enhancements made from the original Invisalign system. Your type of problem was not effectively handled with the original Invisalign design.  The later Invisalign design, however,  incorporates power ridges that can better create torque on the teeth to correct your type of problem.  The aligners can also do some widening of your dental arches at the same time.  Your Invisalign dentist may show you a simulation of the changing positions of the teeth with each aligner to satisfy your need to visualize the process before treatment.  So the answer is Yes, Invisalign can handle your teeth repositioning quite well.

For sure, you need more expansion. Your upper teeth need to ;be expanded. Expansion will make more room for your teeth. Expansion will also look better as you develop a wider smile. Expansion will prevent cheek biting.

To keep your front teeth from flaring out too much and to prevent the buck look you need to wear elastics with Invisalign. Elastics will also distalize your upper teeth as the lowers come forward somewhat. 

The bite will open as your teeth are expanded and as your upper and lower teeth are depressed with Invisalign.

My patients get excited about Invisalign because they offer the patient the opportunity to view a computer simulation of their treatment from the beginning to the end.  Since you are a visual person ask your dentist to view this simulation.  Its called a ClinCheck.  Good luck