The 115's with a 243 will run 1k in fine fashion. I would recommend at least a 7.5 twist if you are planning to shoot said bullets . . .
Agreed. I had a tactical competition rifle built for my small-framed daughter in .243. We used a 1:7.5 Schneider barrel and shoot either 115 DTACs or 105 Scenars and it works VERY well to st least 1,200 yards. Because recoil is light, we were able to make the rifle light and portable and it is quite comfortable for her to carry and handle. It actually comes very close to my 6.5-284 for trajectory, although energy is down with the lighter bullets, and the lighter bullets will blow around just a little more.
The biggest issue with your SPS, assuming it shoots well enough to effective at extended range, is going to be the (too slow) rifling twist rate of the factory barrel.
Heavy bullets are needed for best performance at longer distances, and the twist rate needs to be rather fast to fully stabilize them. Even if they don't actually turn sideways, good stability is important to realizing the BC built into the bullet. If the bullet is only marginally stabilized and nutates in flight, the BC is compromised and drag, drop and terminal energy will be much more than expected.
Even a new rifle is going to need custom work in the form of a fast-twist barrel, so your SPS will likely be a decent basis for having the work done.
If you're planning to hunt with it as well, you might consider the .260, which delivers about the same trajectory, but more energy at the longer distances by virtue of it's heavier bullets.
A workable compromise between a good hunting rifle and a good rifle for extreme long range may prove tough to find. First, we have weight and stock styles to consider, and a good prone rifle for long range is going to be a little unwieldy. Then, bullet performance may be an issue, since a hunting rifle with good quality hunting bullets may not deliver the long range performance of the long BTHPs, but those highly efficient BTHPs may not deliver the on-game performance one needs for humane hunting.