killer,
Your on the right track with H-1000 and the 110 AB. It's proven to be one of the more accurate combos in my 257's. Additionally, H-1000 is an Extreme powder and not temp sensitive.
My go-to load combo however, is RL-25 and the Nosler 115 Ballistic Tip. RL-25 is magic in the 257. It's absolutely provided the best combination of velocity and accuracy in all 3 257's I've owned. Should find your sweet spot between 69.5 and 71 gr. Expect velocity to be in the 3300-3450 range with 115's. Don't fret about bullet construction with the BST. Even driven at 3400 fps, it's held up splendidly on thin skinned game. It's much tougher than most give it credit for. Plus, for a .257 caliber bullet, it has a decent BC of .453, which is much better than most other .257 cal offerings.
As for seating, I typically always find my best accuracy when the bullets are seated deep...less than 3.20. This holds true for the 110 AB as well.
One point of interest to pass along in regard to the 110 AB. Be vigilant when approaching max loads using this bullet as it seems to be much more susceptible to pressure spikes than other bullets. I've never experienced this issue with the 115 Ballistic Tip.
