Wildcats based on .444 brass do not necessarily operate at lower pressures and in fact are approaching the ragged edge of Contender safety, particularly with the .309 JDJ.
The .375 JDJ, if loaded to .375 Win ballistics, would of course be operating at lower pressures due to the greater combustion area. But why have a JDJ if you shoot .375 Win level loads in it?
Loads listed by J.D. Jones for both the .309 JDJ and .375 JDJ, along with the ammo now offered by TC, operate at pressures equal to or even slightly higher than .375 Win factory ammo.
If the .375 Winnie was not safe for the Contender, you can rest assured that TC would not have chambered for it or continue to offer it through the custom shop.