That would be my guess. You will serve yourself well to get into reloading. There are some great bullets to take advantage of that aren't offered in factory ammo. For instance the 150 Bergers for the 270 are great and fly very well out of my 270. Also for the 30-06, there are a number of heavy bullets that would put you well past 1000 yards.
Handloading the 30-06 is an excellent option, especially if this rifle will pull double duty as a hunting rifle.
The case has lots of capability to sling the heavy, high BC bullets (190-210gr class) very quickly and it's easy to find ammo for it.
One thing that I advocate for a hunting rifle, especially something that may end up in a hunting camp 20 miles from any kind of civilization is:
Chamber it in something adequate, but not a wildcat or uncommon caliber. 30-06 has the benefit that if you dropped your favorite hunting ammo in the lake or left it at home, you could walk into practically any hardware store, gunshop, or Walmart and find a box of hunting ammo (probably several options really) that will kill anything on this continent and shoot well enough in your rifle to get the job done.
If you wanted a good balance of knockdown power (good bullet weight) and high BC's then a better option is the 280 Rem, which is just a 7mm-06
Factory match ammo is next to impossible to find, but you can get factory hunting ammo for it. The high BC 7mm bullets out there are exceptional and the 06 case has the same useful capacity as the SAUM series, making it more than capable to sling them hard for LONG shots.
For practicality sake, mainly based on widespread ammunition availability, I'd put the .30-'06 first.
The .280 Rem follows, and I think that the Hornady Custom 139gr SST .280 load is a good commercial choice. On paper, it's quite adequate to reach 1Kyd supersonic, and I find it quite accurate at the shorter distances I've been able to shoot it, out of factory Rugers.
Shooting targets to 1000yd is a bit different from hunting to 1000yd.
The former requires good shot placement, the latter requires that and also requires it to be followed up by good terminal performance.
I would be a bigger fan than I am of 1000yd hunting if I had more faith in the ability of less than magnum chamberings to deliver adequate terminal performance all the way out there
My chosen solution to this is to stay with the non-magnum chambering, approach closer, and increase the advantage that a nearer shot provides in both placement and terminal performance.