1/8" of wear over 12" will almost certainly cause the chain to not mesh well with the cogs. Changing the chain would be a mistake and almost certainly make the drivetrain skip under pedalling load.
Also, there is no damage caused by running a slightly long chai, even if it's dragging over the derailleur jockey wheels or front derailleur cage - unless you ride like that for a long long long time. When I used to assemble bikes I would adjust the limit screws on the front derailleur so it made a bit of noise when cross chaining (either big-big or small-small) as a kind of 'alarm' that you were in a bad gear. If the chain on your bike makes noise when in small-small, just treat it as a reminder not to cross chain.