Project Online Site task list not showing the fields I want to see

[JGrantTyler]

I have a SharePoint site template with a task list with many fields from our project plans and views for filtering those tasks.  When I use the site and project plan templates in an Enterprise Project Type and create a new project using that EPT, the project plan does sync into the task list, but all of my preconfigured columns and views  are no longer there.  Is there a way to add columns that exist in my project plan into this SharePoint tasks list?  I don't see them in the columns listing when I modify a view or go into List Settings.

[#2]

Let me clarify my question: My MS Project plan has many columns, including custom text, number and flag columns used for various filters and views. The site task list created from Project Online does not have the same columns I have either in a) the project plan or b) the site template used to create the project site. Instead, there are a few useful columns, and many of the columns I need to have in SharePoint are not available on the Site.