Power Query - How to move data to new row and new column?

Here's one way to do it in the query editor.  To see how it works, just create a blank query, open the Advanced Editor and replace the text there with the M code below.

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMlTSUQrJyMxLVwCxDA2AhIVSrE60khEuCWNMCUuwBMIokF5DQyxGgSWMsBgFljCGGBULAA==", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [#"Part Number" = _t, Part = _t, Depth = _t, Height = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Part Number", Int64.Type}, {"Part", type text}, {"Depth", Int64.Type}, {"Height", Int64.Type}}),
    #"Unpivoted Other Columns" = Table.UnpivotOtherColumns(#"Changed Type", {"Part Number"}, "Attribute", "Value"),
    #"Added Custom" = Table.AddColumn(#"Unpivoted Other Columns", "Custom", each if [Attribute] = "Part" then [Value] else null),
    #"Filled Down" = Table.FillDown(#"Added Custom",{"Custom"}),
    #"Filtered Rows" = Table.SelectRows(#"Filled Down", each ([Value] <> "Thing 1" and [Value] <> "Thing 2")),
    #"Added Custom1" = Table.AddColumn(#"Filtered Rows", "Dimension", each if 
[Custom] = "Thing 1" and [Attribute] = "Depth" then "Depth" else 
if [Custom] = "Thing 1" and [Attribute] = "Height" then "Height" else
if [Custom] = "Thing 2" and [Attribute] = "Depth" then "Width" else
if [Custom] = "Thing 2" and [Attribute] = "Height" then "Remove" else null),
    #"Filtered Rows1" = Table.SelectRows(#"Added Custom1", each ([Dimension] <> "Remove")),
    #"Removed Other Columns" = Table.SelectColumns(#"Filtered Rows1",{"Part Number", "Dimension", "Value"}),
    #"Pivoted Column" = Table.Pivot(#"Removed Other Columns", List.Distinct(#"Removed Other Columns"[Dimension]), "Dimension", "Value")
in
    #"Pivoted Column"

Pat