Arranging values from Series of Arrays in Descending Order by Formula - Not Macro

Hi John/Jason,

Thanks again for spending time on this for me and for the revised formulas. I hate to be the bearer of bad news because what you both have produced has exceeded my abilities, but I've found the following problems:

John
With respect to the latest formulas you provided, the second and third ones are generating blank results. The first and fourth are working as expected. Please see the attached.

Can I also ask what this part of the formula is for - (INT((ROWS($1:1)-1)

Jason
I have adapted your formulas to my real spreadsheet. Just to remind you of one of the comments I made earlier, I said
"Please note that the number of departments can increase or decrease month to month so the solution must have the flexibility to list "Expense Type 1 - Dept. 4" should Dept 4 ever be added."

Using your first formula as an example, this is not possible. The reason why is in red below:
=IF(B15="","",IFERROR(INDEX($C$3:$K$3,IFERROR(MATCH(B15,$C$3:$K$3,0),1)+((COUNTIF(INDEX($C$5:$K$7,0,IFERROR(MATCH(B15,$C$3:$K$3,0),1)),"<>0")=COUNTIF(B$15:B15,INDEX($C$3:$K$3,IFERROR(MATCH(B15,$C$3:$K$3,0),1))))*2)),""))

The problem being that the array in red assumes only 3 rows, where in fact there may be four or five in coming months. Therefore I amended the formula as follows (again see red):

=IF(B15="","",IFERROR(INDEX($C$3:$K$3,IFERROR(MATCH(B15,$C$3:$K$3,0),1)+((COUNTIF(INDEX($C$5:$K$10,0,IFERROR(MATCH(B15,$C$3:$K$3,0),1)),"<>0")=COUNTIF(B$15:B15,INDEX($C$3:$K$3,IFERROR(MATCH(B15,$C$3:$K$3,0),1))))*2)),""))
but the problem with this is that the journal list is now generating 'x' number of lines for each expense type where 'x' is equal to the number of rows in the array (red above) less those rows in the array which contain a zero value for that expense type.

And as much as your last comment made me laugh (I got some strange looks having just burst out laughing for no apparent reason) I wouldn't want to put you through that again, so if it's easier to generate a formula for the 'Satisfactory Solution' this would be great. John's seems to be almost there, so if either of you can look into the problem I outlined above, that would be fantastic.