Move the cabinet up.

The easiest option would be to remove the over the fridge cabinet and replace it with open shelving.

Check though and see if that is the overall height including the hinges or the height of the refrigerator carcass itself. Sometimes the hinges stick up about an inch more.

For only 1/8" you can see if the bottom of the cabinet can be trimmed. We did this in the old house...there was a lip on the front and the part that was the bottom of the shelf was recessed up inside, so they were able to trim just the front board and it fit. If not, then look into getting the cabinet modified some other way. For such a little bit, you should be able to find a solution.

I don't remember who this fridge belongs to but here's a good adjustment - open shelved, just cut down the cabs or a combination of the 2 -

Trim the cabinet. You should have 1/4" easy that can come off if you've got framed cabinets.

You can remove the feet on the bottom of the frige. Or, you can remove the plastic hindge on the top to give you the amount that you need.

This is what we have going on now with an old fridge, new fridge taller. We can't modify tese cabinets as they are custom, and we don't know where they were ordered. I'm open to an open shelf idea, since I can't reach in there anyways, I'm just worried that it will look unfinished there

I'd double check the specs. As mentioned above, the hinges at the front are taller, usually the height that is listed. The body is likely shorter, and you may be ok if the cabinet only covers the body. Or you may have to trim just the first few inches a bit if they cover the hinges.