If it's skipping on a cog, it's the cog not the chain. A new chain will be more likely to skip on a worn cog than will a worn chain. The amount of wear that causes skipping is pretty small and difficult to see by eye. Autoshifting is a separate problem unrelated to the chain, IMO.
I don't know what an "LTH" is but it seems odd that the new chain was shorter rather than longer and that 1 link shorter (1") was OK. Does an LTH have unusually long chainstays?