Ordinarily I would question whether push feed or CRF really makes a big difference but for a 404J I think it could. The shape of the cartridge and the fact that it's beltless and "rimless" can spell problems for extractor to snap over on the rim when bolt is closed. Snap over can even be a problem for CRF (ask me how I know!) due to the 404J's sloping shoulder and no belt, especially if loading dies aren't set up properly or case rims aren't consistent thickness ( = RWS brass!). Then the cartridge can be pushed forward into the chamber without catching the rim and cause a jam. At least with CRF, 404J cartridges loaded from the magazine shouldn't be a problem. But push feed rifles require snap over even when loading from the magazine. It's a theoretical problem anyway. Remington went with beltless 404 case (almost) when they developed their RUM line of cartridges and they only make push feed rifles, but they put a sharper shoulder on the RUM cartridges (I believe 375 is the largest caliber in the series vs 404J's thicker .423 diameter bullet). Anyway, I wouldn't hesitate to build a belted 375 H&H on a push feed action but might think twice (at least) before using push feed to build 404J. But that's just me.