Griz : The 223 is one of those small calibers where primers can really make a difference due to primers burning rates. To save yourself some bucks go buy one pack of each primer cci, fed, rem, win, and wolf if you can find them. Repeat find Wolf is you can find them, some some people will say oh there Wolf and junk not true they are very hot and extremely consistant in the sm rifle size, and probably one of the reasons I'm getting best groups with ball powders.
Now I don't always use the same cases generally I will use win cases in the Ruger and WCC-84 military in the AR mainly because I have buckets of it. Nothing wrong with the other brands as long as you use the same brass and don't mix between rifles, keep it seperate. Use all the correct loading techniques and trim lengths. I do crimp the 223's with a Lee collet crimp, probably not needed but I like it for feeding in the AR so I just do it in the ruger also.
Take one specific load and strictly test primers. I think you will be surprised in accuracy difference just by changing the primer. I see this more in smaller cases like the 223, but it does carry over to the large mags.
H-335 is OK it's not my favorite even though a lot has been written on it and several friends use it mostly not to their liking once they switched to a few other powders. I really like Ramshot Tac & BLC2 as do a couple friends, yes they are ball powders with either Wolf or CCI. Best groups were TAC & Wolf. Followed by Tac- CCI, BLC2 -CCI, I have also had good luck with IMR & H-4895, Varget was so-so.
What I would do if you have any H-335 left is get yourself some Hornady 50-55's whichever, flatbase at these shorter ranges almost always shoot better. Pick an oal like 2.200 these are very short bullets so there isn't a lot of leeway, take 5 junker rounds to foul the barrel and load up all these different primers at one grain under max and shoot them. Yes I know you are suppose to work up but there ain't a whole lot of difference in these small cases, if you don't feel comfortable split the difference between high & low powder charge. Don't clean the rifle just shoot them, clean it later when you get home. Keep them seperated in 5 or so different zip-lock bag and marked with load & primer type for when you get home to look carefully at cases & primers. Take your target and bring it home also, and put it in a folder for later reference with environmental conditions , wind , temp, date, load data, oal, volocity, rifle type, etc. You will be surprised how many times you will come back to that target later. Normally what I do is I have a 2" square stencil made up and mark 9 squares on the back of a plain target with a heavy sharpe. I do use other lined stencils whichever you can see the best and be the most precise will work.
What his is going to tell you is does one primer work over the others with a specific powder. You may luck out and find a really decent load to fine tune charge weights and seating depth later. If none work or are so-so switch powders and try it again with different primers. I'll bet by the time you get to that last bullet and used a couple powders & primers you will have a pretty good load or two that stands out to fine tune.
I'm not one of these that will sit there and shoot every five minutes, I shoot one right after the other for a specific test usually 5 rounds, I walk down and look at the target, and let the rifle cool down. One reason I want to see if it's walking shots especially on a new rifle. 20 shot at 4 targets in 30 minutes test it like you would shoot a match. I really think you can get this rifle down without a whole lot of testing, unless you run into a bedding problem. Anyway good luck and keep us posted on how it shoots. Ron