Consolidate Continuous Date Ranges into one record

OK, I think I have this. First, in your query add an Index that starts at 1. This is my query (Enter Data).

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMlTSUfLKz8gDUsG5mSUZQNpQ31DfyMDQHMI0hbFVDA0M9AwMFJRidaKVjLBqM0PoMzLAqs8Ymz4jJPuMjLDqM8GqzxRJnzlcnylUWywA", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type text) meta [Serialized.Text = true]) in type table [ID = _t, First = _t, Last = _t, #"First DOS" = _t, #"Last DOS" = _t, Paid = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"ID", Int64.Type}, {"First", type text}, {"Last", type text}, {"First DOS", type date}, {"Last DOS", type date}, {"Paid", Currency.Type}}),
    #"Added Index" = Table.AddIndexColumn(#"Changed Type", "Index", 1, 1),
    #"Reordered Columns" = Table.ReorderColumns(#"Added Index",{"Index", "ID", "First", "Last", "First DOS", "Last DOS", "Paid"})
in
    #"Reordered Columns"

My table created by this query is called "Problems". OK, now create the column as above, here is the code again:

Column = 
VAR mydate = MAXX(FILTER(ALL(Problems),Problems[First DOS]<EARLIER(Problems[First DOS]) && Problems[First]=EARLIER(Problems[First]) && Problems[Last]=EARLIER(Problems[Last])),Problems[Last DOS])
RETURN IF(Problems[First DOS]-mydate = 1,1,0)

Now create this second column like this:

Column 2 = IF([Column]=0,[Index],
VAR myindex = MAXX(FILTER(ALL(Problems),Problems[Last DOS]<EARLIER(Problems[First DOS]) && Problems[First]=EARLIER(Problems[First]) && Problems[Last]=EARLIER(Problems[Last]) && [Column]=0),Problems[Index]) RETURN myindex)

You should end up with a table like this:

Now create a Table visualization in the Report pane and place First, Last, Earliest First DOS, Latest Last DOS, Column 2 and Paid and you should get this:

Probably a more elegant way but this is the first thing I thought of. I was trying to account for the possibility that the Index may not be contiguous between rows in a sequence but I may not have thought of every possible boundary case.