Cast bullets in the 500+ grain range. I think you'd be pleasantly suprised with the accuracy of black powder loads. If black powder is not a consideration, then, I have always felt that they made IMR 3031 with the 30-30, 30-40, 38-55 and 45-70 in mind. I've tried 5744 and it shoots good but too much residue to me. Ive used IMR 4198 with good results.
But this particular rifle deserves the best, give black powder a try, I think you'll like the results.