"....Does anyone have experience with the "Safari" or "Dangerous Game" cartridges? I've mainly become interested in 375H&H and 416 Rem. Is the recoil really that much of an issue when you don't try to sit down and fire of 20 from the bench? Any other 'practical' big boys?...."
375 H&H, 416 Rigby, 458 Lott.
If you are a student of recoil management and get your rifles done right,then not much problem on the recol front. If you prefer the American, "Don't want to take the time (or money) to understand and address the fundamentals, just give it a shot and hope for the best, like the school of hard knocks" approach, then recoil could be a problem, especially at the bench, but also standing.
Beyond that, I don't know enough about your current rifles or your possible uses for said rifleto be able to make a recommendation.
For a much more robust discussion go to
http://forums.accuratereloading.com/eve/forums/a/frm/f/4711043