Go to the Alliant and Hodgdon sites and find powders that give the velocity you want. Then try to find them. I have a batch of Herco, and it is clean burning. So is Universal. Winchester Super Handicap is turning out to be my favored powder for 1250 loads with 1 1/8 oz of shot. Herco is sparsely available, but hits the racks occasionally.
Herco can go to suborbital speeds with 1 1/8 oz loads.
When getting in the 1300 fps arena, make sure recoil does not become an issue. If your gun is on the heavy side and fits, you should be fine. I bought a small sample of Winchester's Diamond Elite 1300 1 1/8 ouncers, and recoil was there, but not pronounced. It would hammer a target that was far, far, away.
Using a Full and Super Full choke in the Krieghoff seems to work well with my preferred load. I never run out of choke, and the 1250's do the job on 60+ yard targets. The courses I prefer do not have targets under 35 yards or so, and can hit the 60-70 yard mark pretty fast.
Do yourself a big favor and follow the loading data closely. Ammo at this level is at the top of the pyramid and must be used as listed. Do not try to re invent the wheel and damage your gun.
Many folks do not see the need for these loads, but there is a place for them on the Sporting course. We want harder, faster, longer targets, and savvy target setters and range operators are accommodating us. I recently shot at a station where the lead was the length of my car, a Kia Soul. I did not skip that station, and judging from the empties there, a lot of folks had the same thirst for this type of target. Ammo must be up to the task. If I shoot the short course I take my 28 or 410.