I'm having trouble fully understanding your question, but the answer is this:
The only ways to interpret text as a range are INDIRECT and VBA.
Otherwise, you have to know where the data will be ahead of time or edit the formula directly.
Let me try offering one other solution. The only reason I can think why you wouldn't edit the formulas directly is that you don't have access to edit that sheet, but you can get 1-time access to set the formulas. If that is the case, you can simply direct those formulas to look at your own table on your sheet, and then put the formula I gave you there.
For example:
In report!C12:
Formula:
=INDEX('MatrixArea'!$D$4:$D$6,MATCH(A12,'MatrixArea'!$A$4:$A$6,0))
and then in MatrixArea A4: "Onion" and in MatrixArea A6:
Formula:
=INDEX('2016'!$D$4:$D$6,MATCH(A12,'2016'!$A$4:$A$6,0))
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