Try a 300 Weatherby Mag. The 300 Win Mag is a compromise of sorts, case volume too small and neck too short, not sure if it was to stay withing a rifle size constraint or the production equipment. - You should get up to 200 fps more with better accuracy.
You WILL RELOAD. Even Walmart charges $40 for 20 rounds, although once you buy the brass the cost difference in reloads between it and the Win Mag is negligible.
With a 220 gr, bullet it'll take down any N. American animal, fast, and the lighter bullets/lower loads are fine for deer.
Best of all I got a Weatherby Vanguard in 300 Wby for well under $400 at Walmart.