It is a Rossi single shot .243. What ammo are you using newt?
I figured. I can 100% for sure say I feel your frustration. I load my own ammo. I started with a 85 grain sierra hpbt loaded over different charges of varget. I got the groups down pretty good, good enough for hunting out to 100 yards, after some time spent with how much powder to put in. The main issue with the rossi is the extreme "jump" to the rifling. The hpbt was only allowing me so much room to seat it out so that did not help at all with getting tight groups.
Then I started doing more research and found that some people were talking about powder dynamics on bullets and so on and so forth. But it got me to wondering if I should use a slower powder and heavier bullet. The heavier bullet would hopefully allow me to seat out further (it did a little), and the slower powder might help with the "turbulence" as it was so called.
So I bought some H4350 and some 100 grain Hornady RN. I have only played around with 3 different loads, but I was happy with one of them and decided to stick with it for the time. Eventually I will play some more, but thats the fun of it. Taking a gun that makes you so mad you could use it as a tomato stake and making it a decent shooter.
One other thing I came across is the thought process of some with the "bullet jump" in long throated rossi. There is a theory that instead of trying to seat out close to the lands, then rather let the case neck hold the bullet solid for a solid start. Of course there are a lot of opinions on this, but I am going to try it sometime without trying to seat so far out to the lands and see what the difference is.
I think the major thing about the Rossi is the flimsy barrel, the fit of the receiver to the barrel (which is what the case head sits against), and the forearm fit on barrel (probably the least of the three).
This is not saying that the Rossi could be a real good gun. It will never stack up against a good bolt action. But at the very least there should be a long wait between shots for letting the barrel cool. And in reality, the first shot when hunting is the most important. I think that this is where the most problems are had. I think that when the barrel heats up after the first shot (and it does a lot), then the forearm touches the barrel a little different (causing some harmonic difference), and the receiver contacts the chamber a little different, and then last but not least the barrel more than likely expands a little. Probably not to a degree that we can detect with common equipment, but a little none the less from the cheap metal it is made out of.
I am going to test the theory by shooting one day and only taking a shot about every hour or so. One other thing is the inside of a new barrel. It is ROUGH. If you pull a piece of cotton through it there will be pieces left behind. I took some time to run very fine steel wool through the barrel and smooth some edges.
I know that was more of an answer than what the question you asked, but I thought I would post it anyways for those who may come along later and are curious. Its a gun, it can shoot, but its not a target gun. I would only call it a hunting gun.