Would you believe we have the same navigation problems in the MH-47G? We have dual EGI(GPS)/ INS, Doppler, four-axis auto pilot, and the ability to couple TCN, GPS, ILS (even back crs), VOR, etc. Still, technically we aren't allowed to conduct GPS approaches in the terminal area because our data base is "corruptable." We can couple our ILS and it automatically levels off at 50' AGL if you really have to get down.
Our SOP is to navigate the airway system and approach using traditional nav aids/needles(coupled of course with the flight director), but have the GPS flight plan overlayed on the moving map to see if there are course deviations. At some points there's as much a 1.5 nm deviations between GPS nav and radio nav. We will usually go with the erred radio nav since that's what ATC is using as well.