Do you reload? Handloading opens up many more options.
There are still many commercial options based on the .404 Jeffrey case... ie. the RUM's, WSM's, Nosler's.
You say you have the "action," so I assume that you have not committed to a bore diameter yet? If the caliber is still open, I would decide what you hope to accomplish with this build, what it's likely use will be and then go from there. Do you have a bore preference? Will you hunt medium game at long range? or large game at medium range? Is this to be a dedicated purpose rifle, or an All-around rifle? These will influence which direction you go with your build... are you thinking a more traditional build in a Walnut stock, such as a Safari iteration, or a stainless modern build with synthetic stock?
I would personally be looking strongly at the Nosler case... there are lots of caliber options now and proper headstamped brass, albeit, not cheap. Performance will be excellent... I would choose something between the .26 and .33, but likely the .28 or .30... pick a fast twist barrel and seat heavy high BC bullets out long, as you have plenty of room to do that... might as well take advantage of your platform.
Just some thoughts.