The problem in this story is whoever made you think you could hit anything at 300 yards without zeroing the rifle yourself first. If that was you , you need to find someone who shoots at that range who can guide you. If not you you need to not listen to whoever gave you the idea.
I zero a rifle first at 10 or 25 yards depending on the range I am at. I then move to 50 yards. Then 100 yards.
I'm not sure how many rounds I fired out of rifles before trying longer shots. Out of 22s it must have been well over 1000. At least a few hundred out of center-fires. I'm nowhere near the skill of many shooters on this board. I rarely shoot beyond 100.
I don't recommend you buy another centerfire rifle if you want to learn to shoot at 300 yards plus. I recommend you buy a 22lr. I have a Marlin 891. It was a great rifle to start, but I have worn some of the components out in less than 10k rounds. That is more than most of them will see in several lifetimes and I have saved thousands over firing all those rounds out of centerfire guns. I think it is about the cheapest target rifle on the market. Like almost all the rifles I own I ditched the stock sights and bought a wiliams aperture sight. I will probably replace it with a CZ.
If you want a centerfire the above offered suggestions are great ideas. If you want on that is military surplus there is only on suggestion I have. The
Swiss K31. The price tag is above your MN, but probably well below the cost of accurizing your MN. The surplus ammo, GP11, is about 50 cents a round. That probably sounds expensive, but it is true match ammunition. You won't find match grade ammunition for any cartridge cheaper. Feed GP11 through a good K31 and the material won't be the limiting factor.
I will again recommend an Appleseed clinic over a CMP clinic. I shot in a CMP shoot weekly for a while. I wold go back if not for my work schedule. The shooters there were the most friendly,welcoming, and helpful of the competitive groups I have shot with, but the clinic I attended was not marksmanship centered. It would be a great place to go shoot weekly after completing the Appleseed though. That is advice based on one CMP group, one clinic, and one Appleseed. Others experiences may be different.
At any level the required rifle, sights/scope, custom stock, bedding, truing, and all modifications required are CHEAP compared to the ammunition it takes to get there and stay there. Don't hamstring yourself by trying to force a rifle to work.
Don't sell the MN though. It is a great solid rifle that, with minimum care, will be here long after a Ruger American stock has fallen apart. Once you learn to shoot at 300 yards with an accurate rifle, with a decent trigger you can lear to shoot the MN at those ranges more easily.