You don't need any FMG to fly the approach because you have the VOR.
If you use the RNP as sole guidance you are doing an RNAV approach, and must comply with all of the requirements therein.
You should probably get your hands on an ICAO PBN manual. It sounds to me like your company is doing RNAV approaches without RNAV approval and without complying with any RNAV requirements.
To use RNAV as a reference the approach must be encoded in the database as such, the tracks and distances must be checked, and nothing from the FAF in can be changed laterally for LNAV, or vertically if you're going to use VNAV. GNSS is required for any 0.3 approach (for now anyway) and RAIM must be confirmed before completing the procedure. There must also be an alerting function in the airplane that warns you when GPS is lost or the EPU exceeds the RNP for the approach.
Do you comply with any of this when you do your VOR approach using the FMGS as the only reference?