I cut out a small section behind the frig. I apologize for the dust, didn't have the shop vac handy prior to taking photo. First image shows a group of wires and just next to it is the 3/8 dark "clear" tubing for the water. The more I think about it, the better off I am just replacing it and not waste time trying to fix it. Also you can see the rubber sealant they used to keep mice out. It isn't an easy task to remove. Just next to the wires I cut all but the part where it is secured on the bottom and it still wont break free.
As you can see there are not any accessible points. If the tubing won't pull from this area then I'll just poke another hole on the inside for the new tubing to route through. Should be able to blindly push new tubing in and use that new opening as a way to route under the sink.
Again, I am appreciative of every ones input so far. I have come to realize I'll just be wasting more time trying to clean tubing that should just be replaced in less time.