Trying to do a sumifs with mutiple text critera that can change

I have a spreadsheet where a large and variable amount of data gets downloaded in one sheet, in another sheet I have the formula to get the sums of the data based on the criteria. The values of the data are all in column G and there are 2 criteria that I am using to calculate the sumifs. The first is in column a of the data sheet and the second is in column M of the data sheet. Column M is actually the month number but expressed in text format so month 1 is expressed as "01". This data comes from an outside source and cannot be downloaded as a number. The formula I am using is =SUMIFS('DATA-ACT-YTD'!$G:$G,'DATA-ACT-YTD'!$A:$A,$A9&"-"&$A$4,'DATA-ACT-YTD'!$M:$M,$A$448) where DATA-ACT-YTD is the data sheet. A9 is the criteria representing a fixed value for that sheet. What I want to do is have a formula that covers multiple months based on what month we are in to get a year to date value. A448 to A462 contain all the possible months. I have managed a formula for these so they will only contain the months I want. I can get the correct result by adding multiple sumifs but this makes the spreadsheet large and unwieldy

This formula =SUM(SUMIFS('DATA-ACT-YTD'!$G:$G,'DATA-ACT-YTD'!$A:$A,$A9&"-"&$A$4,'DATA-ACT-YTD'!$M:$M,{"02","01"}))*$B9 will get me the correct values for months one and two. However the amount of months that I want to add up is variable nd I can't find a way of having a vriable set of text fields within the braces, any help appreciated.

File is huge and calculates loads of financial data.

All help gratefully received

Ok I have done a small sample of the file with the numbers anonymised. Please note that there are normally a lot more sheets and considerable more data. One of the problems is the size of the file.

The cell in A6 on the HL tab is downloaded from an outside source and that is what drives the month I have to use. I chose that cell by setting it in the outside source. The data while not all data is in exactly the same format as is downloaded and that format cannot be changed.

OK tried that either I am doing something wrong or that doesn't work (i'm probably doing something wrong). In effect the months to be used are currently calculated so I have moved that set of calculations to the Lookup period tab in J1 to J14 and then added the formula you suggested in cell G3 on the HK tab but even entering it as a array formula it just gives me an error. I've attached the revised spreadsheet.