My understanding of Cutler is that we take supplements off round as well as on round, including minerals. That is what is suggested in the large yahoo detox groups as well.
Certain minerals are problematic when chelating with EDTA but that is not Cutler's protocol for mercury lead and arsenic.
You'll probably avoid high thiol foods and supplements while taking ALA since ALA increases the thiol pool. Too many thiols tends to be problematic for roughly 40% of Hg toxic folks, esp when taking more generous amounts of ALA.