OP, 300 yds for that rifle should be very doable with several types of good bullets.
The 6.5 mm has become extremely popular over the past ten years, starting about 50 years ago, when the 6.5x55 Swedes started coming into Canada.
The biggest issue I see with your rifle is the short barrel, as velocities will be much lower than most manuals indicate for their loads.
Paul T is correct about the bullet weights that will work in your rifle, but I believe even heavier/longer bullets will stabilize well enough for the ranges you shoot.
You're going to have to try to find ammunition the rifle likes by trying as many as you can until the rifle shoots one much better than the rest.
The biggest issue you will have, barring money, will be the availability of commercial loads with ELD, VLD, and ELM bullets.
Muzzle blast from that barrel is going to be distracting at best. Evening shots will be spectacular and "enlightening."
If you don't reload, now would be a good time to start.