Well aware of the two problems outlined- as for the former, using antibodies or engineered oligopeptides would not necessitate any new metabolic pathways; another option would be to engineer the gut microflora to produce said chelators
As for the latter, from what I could find (admittedly not much) thiol-based chelating agents (dimercaprol) are reasonably selective towards heavy metals- ignoring calcium, zinc and iron; its toxicity having a different mechanism.
Emulating that with a peptide might be possible- and even if simple (mono/bidentate) ligand selectivity is not good enough, the differences between most common heavy metals (Cd,Pb, Hg) and biogenic cations (Zn, Fe, Mn, Ca) -eg. ion radius, ligand preference, charge etc- might (?) be possible to be leveraged (mimicking K/Na selectivity in ion channels- with thiol ligands, for instance): most heavy metals are thiophilic, for instance: and all of them significantly larger than their biogenic counterparts: https://en.wikipedia.org/wiki/Ionic_radius: from the table Iron (the largest biogenic /thiol binding/ 2+ion) is >0.15A smaller than Cd; if we ignore that, the difference with the second-smallest (Hg), 0.25A, approaches that between Na and K (0.36A)- and the significantly stronger ligand-ion interactions of transition metals would likely improve the selectivity
as for the mechanism of action, having a system like this would of course not prevent (even the targeted) metal toxicity to enzymes- it might, however, prevent their accumuluation, or limit the toxicity to a specific location (lead would inhibit M2+ uptake in the gut, but get mostly neutralised once in bloodstream)