Tweak my macro, is there a way to have it move only filtered items?

Well, since your posted code does not autofilter, you might do something like this:

    Selection.AutoFilter
    ActiveSheet.Range("$A$1:$J$631").AutoFilter Field:=1, Criteria1:="Cherry"
    ActiveSheet.Range("$A$1:$J$631").AutoFilter Field:=2, Criteria1:="19th"
    ActiveSheet.Cells.SpecialCells(xlCellTypeVisible).Copy Destination:=Sheets("sheet1").Range("a1")

,etc.