2900-3000 fps with 250 grain bullets is achievable with any of the full length belted wildcats.
Bullet situation is a little better for .358's these days, it's been a decade or 2 since I played the .358 game but those older bullets like the Hornady never offered enough accuracy to be "long range" at magnum velocity, slowed down to Whelen velocities they shot pretty well. The Nosler Partition will hammer a moose, but again I've not seen the consistency required for long range shooting.
I like the idea of the improved Lapua, and the 340 Cutting Edge. I'd start with a custom action with enough size, and a barrel with enough twist.
If going with a standard "magnum length" action, I'd use the RUM case, and see if Cutting Edge would make me something in the 275-300 grain range.
Have fun sounds interesting.