There are plenty of bullets in 30 caliber to choose from that will work great for thousand yard hunting. The first to come to mind are the following:
208grn. Hornady A-Max= .648 BC
200grn. SMK (Sierra Match King)= .560 BC
210grn SMK= .645 BC
240grn SMK= .711 BC
210grn Berger= .631 BC
200grn Nosler Accu-Bond=.588 BC
210grn JLK= .690+ BC
All of these bullets listed are very good bullets for taking deer size game at 1000 yards with the RUM. The RUM can produce enough velocity with any of these bullets to maintain the velocity and energy necessary to take game at extended ranges.
Like Savagshtr said, you can always jump to the big .338's. Obviously recoil is going to be an issue. The 338- RUM, Norma, Lapua, Allen Magnum, Allen AX and a copious other larger .338 with a 250grn (SMK, Hornady BTHP). or 300grn SMK will do the trick.
Remember at extended ranges you will have time to put ear plugs in or put ear muffs on. Shooting these heavy high BC (Ballistic Coefficient) bullets are going to be very high recoiling. You should definitely invest in a good muzzle break which you already said you were going to do. Your current set up sounds really good.
Just make sure that you spend a good deal of time researching and choosing your optics. For shooting long range it is very important to make sure you have a scope that will work well in doing multiple adjustments. I don't know much about Kahle's but I do really like Nikon. I own two Nikon's in the Buckmaster series because I am on a budget. If you are going to look at the higher end Nikon's, let me direct you to research Sightron SIII, Vortex Viper line, Bushnell Elite Tactical series (3200, 4200), Nikon Monarch, and Leupold Vari-X series. All these scopes will work very well.
Hope this helps,
Tank