Soft tops come with door surrounds. These are either the plastic framing or "wings" that you describe, or a simple horizontal and vertical bar (as in the Supertop).
Can you use your doors? Maybe.
With the YJ, the Jeep soft top group and the Jeep hard top group were not on speaking terms. So the hardtop uses an upper door opening that has a rounded back corner, while the soft top group demanded a square back corner.
Bestop designed the YJ Supertop with the hard top style opening, since we sell it mostly to people buying their first soft top.
The factory top, the Bestop Replace-A-Top, and some others out there, are designed to fit with the rounded door openings.
Clear as mud? Take a snapshot of your doors, making sure to get the top rear corner. Send it to email@example.com
, and ask them "will the Supertop work with these YJ doors?"