Conor needs to find playing time as a super-sub, only starting against right-handers. 3B, DH, 1B, 2B, LF are the places I'd try him. I really would not mind seeing him slide over to 2B, but I doubt he has the range for it.
We do have a glut of middle infielders and I think trading Alexei would be a smart move - I'd also offload Beckham if you could get anything decent for him. You can then bring Gillaspie, Sanchez and Semien into 3B SS 2B and see what you have. Davidson I'd wait until at least next season, assuming at least one of those options fails. Leury Garcia needs some more time in the minors.