Does every finitely presented subdirect product of limit groups admit a polynomial isoperimetric inequality? That is, does there exist a constant $C > 0$ and an integer $d \geq 1$ such that for every null-homotopic word $w$ in the generators of the group, there exists a van Kampen diagram for $w$ with at most $C|w|^d$ 2-cells, where $|w|$ denotes the length of the word $w$?