Do you have Process Management ES2 installed in your organization. If so, I can suggest few options.
If you only purchased LiveCycle designer, it is quite difficult to achieve with sign form.
Yes, I do have LiveCycle ES2.
Well, you can have a single form and achieve your need.
Create all the sections including request details and all four approval fields in one form.
Have a hidden field to hold the role which determines which section must be visible at a given time.
Instead of manually assign Project ID, let the liveycle process do that job for you.
Submit the filled form to a general email account and receive it through Email Receive activity.
Assign a Project ID using SetValue.
Set the role for each of the four approvers and submit the form to them simultaneously using branch activity. Send four copies of form.
Receive the approvals and merge the form data into one form.
Hope that helps.
If you need the abstract process, write an email to me email@example.com