VBA to sort a table for values between

Need VBA to sort a table for values in a specific range.
I'm new to VBA but I think it may provide a solution to a problem I have processing some table data. However, as you know learning a new language is challenging and takes a while.

I've tried all the excel standard formulas to do this, but it is a kind of batch processing and nothing in regular excel, formula-wise, really works for what I need. I am attaching an Excel workbook so you can see the problem I have to resolve.

The table data to process is in 9 columns.

After any negative values are removed, each Column needs to be sorted to have all the values in each column in ascending order.

I've been able to get the macro below to do that for me and in my attached sample sheet it has been run.

Sub MultiSort()
Dim Cols As Range, i As Integer
Set Cols = Selection
For i = 1 To Cols.Columns.Count
Cols.Columns(i).Sort Key1:=Cols.Columns(i).Cells(1, 1), _
Order1:=xlAscending, Header:=xlYes, _
OrderCustom:=1, MatchCase:=False, _
Orientation:=xlTopToBottom
Next i
End Sub

Now I need to know how to edit that macro into a new one to extract ranges of numbers to pull those values out and paste them into a new table shown below the first in my example.

The bracket groups into which I want to organize my column data are:
>=1 and <=60
>=61 and <=121
<=122 and <=182
>=183 and <=243
>=244 and <=304
>=305 and <=365
>=366

If anyone can help me I'll be grateful.

Jim