Good advice on bullet types. Partitions are a good place to start to avoid the non-penetrating "blow up" you described. IMHO, if you are moving up to elk, then your quest for a better bullet should be only part of your mission.

Even a cow elk will run two to three times larger than deer and are much more durable also. Little jobs, little tools. Bigger jobs, bigger tools. Everyone should have a "cornerstone" 30-06 in their closet. You might consider picking one up, much better suited for the "elk job" especially since elk are not prone to giving one that broadside (deer) pose.

Also, FYI, in the big picture, mid-bores start at .375 and run through the .416's. 338's down are considered smallbores.

Good luck in your hunts this fall,
EKM