It sounds like you need SUMIFS rather than SUM/OFFSET. If the years are in separate columns you would need a separate SUMIFS for each column and you can control whether the year is included or not using a cell value somewhere.
it might be a long formula as you've got say 5 separate SUMIFS but as long as the SUMIFS is simple that doesn't matter, it'd be less complex to maintain than the equivalent SUM/OFFSETs.
If it needs to be dynamic, you can use OFFSET in it's longer form and SUMPRODUCT with it's vector form
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OFFSET(Anchorcell,Rows down, cols across,number of rows in range, number of columns in range) where Number of columns can be determined by a cell value you input and can be negative so to pick up the last x years you'd base the anchor in the rightmost column and use a -ve number for the cols across value and the +ve number for the range width.
So if you've 1 col of text and 5 cols of data base it in col F and use OFFSET($F1,1,-H2+1,100,H2)
where data is in rows 2 - row 100, and H2 has the number of years to include. If you put in 3 in effect this would be OFFSET($F1,1,-2,100,3) i.e. OFFSET($D1,1,0,100,3) which covers 3 columns D-F
=-SUMPRODUCT(OFFSET(FS!F1,1,-{Number of years of data to include}+1 ,{Number of rows in table1},{Number of years of data to include}),--(FS!A2:A100={label in summary report})
You might need to change -- to 1* if there's blanks or zeroes (I forget which doesn't work with which)