Re: So I finally shot my first rifle reloads.....
Laser, welcome to the addiction. First off, good advice on folks saying tweak the powder charge in .3 gr increments, BUT..
what I would focus on at this point, especially with that bullet (TSX), is the COAL, or specifically the seating depth of your bullet. TSX's (whether tipped or not) are very picky about their 'jump' into the lead (or lands). Barnes recommends having 50 thousandths of jump, or more.
I would load several rounds with the bullet seated 10 thousandths further into the case, e.g. start with the seating depth you are currently using, say 5 rounds. Then load 5 with everything the same EXCEPT seat the bullet 10 thou further into the case. Then 5 more that are 10 thou further into the case than those, and so on...obviously you have to use common sense, and if you KNOW you are already more than 50 thou off the lead, than seat some out progressively at some increment, say 10 thou at a time, maybe 5 thou, until you have some that ARE at 50 thou off the lands. You can certainly get closer than 50 and have good/better accuracy, I do in some of my rigs, but the bottom line is, seating depth really affects accuracy with TSX's especially, IME, and I typically find best accuracy somewher between 30-60 thou of jump.
The next thing I would be looking at is case to chamber fit, I always achieve best accuracy with a case with a slight crush fit to what I call a zero headspace fit, meaning that to the best of my ability the case is sized during the reloading process such that the headspace changes zero from pre-firing to after firing--which is a slight fallacy, as the shoulder move forward a small amount, even with a slight crush fit, but in short, I look for a case that is sized to fit the chamber as closely as possible. The Nosler reloading manual--and I'm sure lot's of threads on sites like this--speak to this type of case sizing--called PFLR (partial full lenght resizing)- it helps when ringing out the best accuracy you can get.
To find out the twist on your barrel, put your rifle in the cleaning cradle/vise, and put a tight fitting patch on your cleaning rod (it has to be a rod where the rod rotates in the handle) and then mark your handle with a sharpie or piece of masking tape or whatever. Push the rod into your barrel until the tight patch just engages the rifling, and then count the turns the rod makes as you slowly pass it through your barrel, and then do the math, i.e. 20" barrel and rod rotated two full times, 20/2 = 10, so one in ten twist in that example.
Keep tweaking with it, that's a lot of the fun-- I will say that in my 270's that I shoot H4831 in, I have found accuracy at a tad higher charge, around 59 grains usually. This is where the previously mentioned ladder test can help, but frankly, I think you are pretty close, and I've never been one to push the envelope on charges, I'd rather find a really accurate load several grains under max, than one a little north of listed maximums!
Beware, next you may be chasing concentricity, or as folks usually refer to it 'runout' which CAN make a pretty big difference--but that's for a little while later, how long just depends on your personal curve, and gear buying appetite!!
Good Luck