I like to think that I have a little more experience with a 260 than most, I have had good luck with what I have done in the past with a 260... And I have and shoot several different 6.5 calibers, I love a 6.5 bullet! take this all as you may, PM me if you want to chat a little more in depth with this all.
I agree with most here on things to check, have someone else shoot it that shoots better than you, etc etc etc thats been said. I have had pretty good luck with my custom 260s that Ive built... Many people have said, and you will read a lot that 260s are a thorn in their side and they cant get them running right...
Now, with the pics you have posted the H4350 is your powder. This is what I run too, as do most people. Your groups with the H4350 are good. I'm fairly certain that your load is in the 41-42.5 range. Play with these loads more. DO NOT shoot them at 100 yards. load test at at least 200 to 300 yards.
Forget about other powders... you got what its going to take already.
I think you said your running a 2nd focal plane scope, make sure your cheek weld is in the same spot every time. A little advice here.. get a little tube of silicone.. lay on your rifle, find the exact spot that your cheek needs to be, take your time.. then put a dab of silicone on the top of the comb there on the stock and let it dry... it peels off easy enough if you don't get it in the right spot the first or even second time.. after it is dry lay on the rifle again and find exactly where that dab of silicone rest on your cheek/face... then every time you shoot make sure your face cheek is anchored with the dab in the exact same place every time... This will give your the best anchor point to insure that you have the exact same hold every time. Some rifles like to be held loose, others like to be held tight, find what the rifle likes and how you shoot best. Get your fundamentals perfect here... easy enough..
I shoot 140 gr bergers and run a 8 twist barrel... YOUR RIFLE WILL NOT SHOOT THESE CORRECTLY. There is a different 260 chamber designed to shoot 140 bergers. 142 gr sierras are more geared towards a 6.5x284, forget about these heavier bullets.
You need to stick with 120gr to 130gr bullets. Brass prep is ALWAYS a HUGE deal with tits cutting accuracy, research and hone in your brass prep skills, its amazing how much of a difference tedious brass prep makes. WHAT BRASS are you running? FL resizing or just neck sizing? Primers? I recommend you use a match primer. Many cant tell the difference using a match primer, but there is more consistency usually. AND CONSISTENCY IN EACH ASPECT IS KEY!
reload 5 rounds of H4350.... 41.0 gr to 45.5 gr in .2 incriments... 41.0, 41.2, 41.4, 41.6, 41.8 etc etc... ONLY LOAD TEST on nice CALM mornings before there is any heat waves, wind or anything... pick the right conditions to test in... just gives you better results and info to go by... When testing take a break between shots, dont heat up the barrel... take your time. make sure to have a heck of a study shooting foundation to shoot from, sand bagged is usually best for me when testing.
What scope rings do you have and scope base? NO ALUMINUM. Metal is just stronger and works better imo. DO NOT have a metal scope ring base, and aluminum rings, or aluminum base with metal rings... its either aluminum and aluminum or metal and metal... cant mix them, both metals have different properties and do not tighten to each other well.
123gr bullets, I think the hornady 123 Amax is one of the most popular. thats what I shoot in a 6.5 grendel. They are awesome bullets if thats what you are using.
Do you have a muzzle brake on it at all? There is a thing called muzzle brake pull off that could be doing this if you do have one.
Some wont agree, but its been working for years for me developing loads, and helped a lot with 6.5 cals... find your max seating depth first... then back off that a hair and test all the loads at this same seating depth.. once you find the best powder charge, then go back and play with seating depth at minUTE changes at a time...
get back to me if you try all this and lemme know what happens. I'm willing to bet that you will see better results if you try this all. Don't jump around on different bullets too much developing loads too. powder charge is going to make the biggest difference here with this caliber. the 260 is finicky, so just relax and take your time. If you find yourself getting aggravated or pissed off during load testing just stop... You will be wasting money as your body wont be relaxed anymore... been there more than once haha.
send me a PM and tell me how you reload, steps you take what you do.. brass prep.. what tools you use to do it etc.. many times there is a key step thats missing that helps a lot with people that I have helped out. I have a few buddies that have seen me run my 260 and have jumped on board and bought 260s too that I have been currently helping out with load development and stuff...
Let me know if I can help you more if you decide that my opinion has helped! in the end each to their own.