the EDTA in the bleach replensiher I would guess is added in along the way to aid in keeping the silver sequestered in the suspension that comes from the silver that is bleached out of the film.
There will be more than just the EDTA; I would suspect there is also something else in it to reinvigorate the active bleaching agent. The other option is that the bleach is reactivated by oxiginizing it (thing fish tank bubbler) and the edta just keeps the building silver levels sequestered.
One of the standard, low-toxic, rehalogenating bleaches used for Lippmann emulsions is based on ferric EDTA. It has extraordinarily good keeping properties several years.
For example:
Fe-EDTA...............30g
Kbr.......................30g
acetic acid.........70ml
(or sulfuric acid.10ml
water.....................1L
Alternatively, the Fe-EDTA can be replaced by 30g ferric (III) sulfate and 30g disodium EDTA.
I guess for the much larger photographic grains you might have to increase the concentration of this bleach considerably.