I would cut a few threads off and do a 7/300 wsm. The wsm case is the widest of any 404 Jefferey.
This is WHAT, I'd DO, too ^^^ in, a New York, Minute !
Just cut a couple of Threads off and re-chamber to 7mm-.270 WSM as it's easier to get .270 WSM Brass and you WILL get, BETTER, Neck / Bullet TIR, "runout" readings, by "Expanding" Necks than, by squeezing them, down,.. and possibly causing,.. "Doughnuts" !
This design is, a Superior 7mm round and is used by, the Canadians and English @ 1,000 Yard Matches !
Only the .300 WSM beats it at, 1,000 yds as, the BIGGER Higher BC, Bullet has, a bit less, Wind Drift !
The 168 gr. HVLD Berger's, would BE,.. "Smokin' !
And it's NOT, an "Expensive",.. FIX, either !
Your Rifle sounds like, a NICE one and well Worth, a couple Hundred Bucks more, to make IT,.. RIGHT !