I don't think you need to worry about anything getting recycled through urine. Even the "lowest quality" urine (with blood, pus, etc.) which must be worse than yours starts to get purified when ingested - that is, whatever is in it, the effect is positive, not vice versa.
Here's a crazy idea - why don't you stop chelating for a while and do UT only? That way you'll know the true effect of UT on you and whether your deterioration is caused by UT or the combination of chelating+UT, for whatever reason.
There's a chance UT is a kind of "chelation" too, you know...
Why do you assume UT can't do what chelation is supposed to be doing?