I would honestly suggest getting a .308 first. Granted, it's not really suited to shooting elk at 1000 yards --- however, it will allow you to PRACTICE a lot more -- and you'll need all that practice before you should be shooting animals at 1000 yards anyway ;)
The thing to keep in mind is the cost to feed your beast: in addition to the per-round cost of the .300 RUM, even if you are reloading, you will shoot the barrel out MUCH sooner than you will with a .308 -- ie after 1000-1500 rounds. I practically feel guilty every damn round I put down my RUM's tube thinking about how I just burned away 1/1000th of my barrel life -- and I can hardly bring myself to practice 'rapid' follow up shots due to 'barrel burn guilt'... (exaggerating slightly here, but you catch my drift...). To put it in perspective, if you take into account the cost of a barrel, getting it chambered, installed, etc -- with the .300 RUM it's like adding $.40 to the cost of every round you fire.
For target shooting, a .308 will get to 1000 just fine with the right load, and your barrel will last MANY times as long as the RUM.
Also, the .308 will be much better suited to most competitions -- for example, 1000 yard F-Class would make great practice (you can shoot in F/TR even!).
I wish I'd been around to give myself this advice a year ago when I started my custom build. I love my RUM, but I just received it in October, and am ALREADY in the process of trading some of my other gun stuff for a .308 so that I can afford to practice more.
As for barrels -- if you are concerned about turnaround time for a custom barrel blank, check out Brux barrels Welcome
-- I've heard nothing but good things, and unless they have recently become victims of their own success, they can apparently get you a made-to-order cut-rifled hand lapped barrel blank in 2-3 weeks.