If C2 had higher splits and power I could justfy using him at catcher despite the low PC. However, given that C1 does have a really good batting eye, I would start him in the 9 hole, let him score some runs, plus even if he's facing a right handed SP, he will still see lot of left handed RPs late in the game and should hit really well against them.
However, all that being said C3 might be your best option if he has a batting eye 60 or higher.
All this is just my opinion. You will get a thousand different answers to questions like this.