Remington, Savage, and Tikka all make left hand Varmint or Law Enforcement models (M700 Varmint, 10 FLCP-K, and T3 Varmint respectively) in left hand. Remington and Savage will be limited to .308 Win. Tikka can be had in 300 WM or 338 WM plus others, but I imagine they would be very hard to find. All models run around 8-9 lbs without scope, should be reasonably accurate for entry level competition and have heavy enough barrels to handle a relays worth of rounds without getting smoking hot. Not ideal for either purpose, but it would be a start.