I have good callouses on my fingers and have been playing acoustic for a few months now after years of electric. Now my callouses have permanent lined indents that make it harder to get the string down fully and if I place the string slightly outside the indent it slips in and makes a horrible click sound.

I've looked about for solutions and people say keep playing but that just seems like it would re-enforce the problem. How can I get around this?

Welcome to the world of acoustic guitar. That happens to all of us.

I usually don't have a problem until the callouses start to scale off, and they snag the strings when I move my fingers from one to another.

You can flatten your fingertips with an emery board of the type used for shaping fingernails.

Just don't sand all the way through, just scale off the top, peeling, layer.
Your guitar is set up badly or you are pressing too hard or both perhaps. Even with an acoustic you should be able to hold a chord with a "heavy hand" rather than a thumb squeeze. Although the ends of my fingers are tough they are not calloused and I don't think they should be. (I play acoustic and electric every day).