I'm going to go out on a limb and recommend Mordekaiser. I know, not a true carry, per say. However, he's one of the few champions that can, if overleveled and well farmed, carry his team, kicking and screaming, right to the Nexus.
He can easily dominate a solo lane against an unskilled or easily intimidated opponent... and it's very easy to intimidate with Mordekaiser.
He can easily out-farm and out-level an opposing lane because he can jungle and lane at the same time.
He can quickly push and apply pressure to towers, and killing towers wins games, not kills.
Just my opinion, take it with a grain of salt. My main reason for suggesting him is durability. Tristana and Ashe are 'carries', per say - but even if fed, can be focused and crushed, leaving your team with no effective damage.