Go to next visible cell without loop
Before you write another line of code, watch this Excel VBA Introduction Part 5 - Selecting Cells (Range, Cells, Activecell, End, Offset).  

Everyone here wants to help you but, and I know that you read this,  you have got to stop selecting and activating cells.  You also need to describe your data.  Posting screenshots wouldn't hurt either.  So if I sound mean but you wrote 72 lines of code to copy maybe 12 values.  

Range.Copy, Range.Cut, Range.Insert and by default act on only the visible cells.

Sub FilterAndCopy()
    Dim Source As Range, Target As Range

    With Workbooks("Epson ASINs.xlsx").Worksheets("Sheet1")
        Set Source = .Range("U2", .Range("U" &amp; .Rows.Count).End(xlUp)).SpecialCells(xlCellTypeVisible)
    End With

    With Workbooks("Epson Itemcodes.xlsm").Worksheets("Sheet1")
        Set Target = .Range("U" &amp; .Rows.Count).End(xlUp).Offset(1)
    End With

    Source.Offset(1).Copy Desination:=Target

End Sub