The VNAV approaches are in the FMS data base under the originally named approach (VOR DME Rwy 22L). When you call up the approach, all of the stepdown fixes are there on the legs page, with their associated altitude constraints. Once cleared for the approach, and on an intercept heading, select LNAV (or LOC if a LOC approach). Once established and at or above the depicted altitude (and cleared for approach), select VNAV and select the TDZ elevation in the altitude select window. This lets the VNAV determine the proper angle and lets the jet fly it. In the case of the JFK VOR DME 22L, it is published to expect a VNAV angle of 3.14 degrees. Read the restrictions on the plate; VNAV is only for authorized operators. Of course this is only for the jet I fly and its associated systems.
I do not see map shifts with FMSs that have GPS & IRS as back-ups. If it was a straight FMS with a AHRS system, much different story, and the PNF absolutely must be in raw data the entire time.