Mark, check this out for an overview over common chelating agents. The document includes EDTA, PDTA, DTPA and others. Note that it is not just important to chelate Fe-III and Fe-II, also the difference in complex stability between the two has an impact.

BTW: When you store your soup at cool temperatures, you also dissolve more air (and as a result oxygen) in the liquid in the long run. This could counteract the slowing down of the reactions you try to quench.