Ideas for precision automation picking up wire

Looking for ideas as to how to face this challenge. I am working on improving a system that feeds one piece of extruded wire at a time into a grinding machine. When it gets picked up and fed, the wire is not perfectly round, and there is variance in its diameter along the length of the wire. The wires are ground to custom size, and come in with typically about 0.02" variance in their diameters. 

Currently, we use proprietary "picker fingers" on a simple linear pneumatic gripper to reach into a stack of the wire, pick one up, and feed it into the grinder. However, this system is incredibly inefficient as the picker fingers are designed for precision (perfectly round, consistent diameter wire) but what they are picking up is not precise. 

The wire diameters tend to range from about 0.035"-0.09". The picker fingers can be changed out, which is what we do currently (a set for 0.035", a set for 0.045", etc). 

If the pneumatic grippers are not precise, the fingers will open too wide and pick up two wires. Similarly, if the ringers are designed too small, they may not pick up a wire at all.

I have designed a few different fingers that we will get machined and test with. Does anybody with experience in manufacturing have any ideas for as to how to pick up one wire at a time, or improve the system all together? I have a few, but do not want to throw them out there and ruin a set of fresh ears/ideas. If you were facing this challenge, what would you do/try? If anyone has any questions for clarification, please feel free. Bouncing ideas and questions back and forth always helps. By the way, I am new to this platform- apologies if I've gone wrong somewhere!