First allow me to congratulate you on deciding on Heym. I believe it is one of the best deals going in this market and would be my first choice for a turn bolt Express style rifle.
404J over the 416RIGBY and here are my reasons.
I prefer the streamlined case design of the 404J over the pronounced shoulder found on the 416RIGBY. Easier feeding for the 404J, even in a CRF rifle this can be an issue.
Sticking with the streamlined theme... The beautiful lines and balance of the Heym Martini Express are done by conserving weight. The softer shooting 404J is better suited to the svelte Heym and I seriously doubt the Buffalo on the other end will notice the difference in energy between the two.
IMO - If you want a 416RIGBY, do it properly with a Rigby Big Game, PH or London Best.
Yes ammo could be an issue. But if you can afford a Ferrari, you should't complain about having to buy the premium fuel it consumes. This goes for any DG caliber rifle.
The Heym is a classic with the current design. It's understated elegance without being overly extravagant. Incredible engineering with the artistic execution of a master. In the end it's what the rifle (and the cartridge) says about you.
Let us know what you decide.