SQL Server Database Fragment Recovery Request

Accidentally deleted SQL Server database folder — only fragmented MDF/LDF recovered. Can anyone help reconstruct?
I own a small restaurant (single-server setup). I accidentally deleted the entire folder with our SQL Server database. I’ve tried several undelete/data-recovery apps; most couldn’t find anything usable. One tool located multiple fragments of the MDF and LDF files (not a single intact pair). The fragments appear to belong to our production DB, but they’re split into many pieces.

What I’ve done so far
Ran multiple file-recovery tools; only one returned MDF/LDF fragments.
No recent full backup beyond an older one (about a month old).
I cannot attach the DB in SQL Server because there’s no single intact MDF/LDF.

What I’m looking for
Guidance on whether fragmented MDF/LDF can be reconstructed into an attachable database.
Steps/tools (commercial or open-source) that can rebuild from fragments, or a recommended professional SQL Server/data-recovery service with this specific experience.
Any do’s/don’ts to avoid making things worse (e.g., imaging the drive, working from a copy, etc.).