Gravity Forms seems to have nearly all the features that I am looking for. There are some features though that I read GF does not currently support. I am wondering if they will be supported soon and/or it would be relatively easy for an intermediate php dev to add this functionality. Time line for delivering the website with these features is 2 weeks, so I do not have much time. Here are the features:
1 - Logged in user can fill out their own form, that is only visible to them.
2 - User can save the progress of the form.
3 - When users log in, they have access to the forms they already started filling in (already in progress) and can continue filling them out
I am willing to pay extra for these features.