[Ron The Plumber]

Sorry to inform you of this, but, unless the fridge sets on the same wall is the kitchen sink, which you indicated it don't, your out of luck on fishing that line through two holes in the floor.

Here is a thought, does the wall the fridge sets against have a bathroom or plumbing on the other side of that wall?

 

[Ron The Plumber]

Did you get the new line installed?

 

[Ron The Plumber]

My answer stands, without access to under that floor it's not going to happen.

Here is an idea to think about, tap into the source from another place, like water heater location, run the line through the attic, over to the fridge wall, and down the back side from above, two small hole in the ceiling, now take a molding strip thicker then the 1/4" tubing and a router, route out the middle and use it to cover up the pipe comming down the wall. Problem solved, this is only if you have attic space.

 

[Ron The Plumber]

If it's easy to access the attic, a couple of hours time, say around $199.99 and you only neeed to run 1/4" copper line.