first of all, if the plates are heavily sulfated, flushing and doing any sort of treatment and then refilling with new electrolyte is going to be problematic.

the reason is
if you are able to break down the crystallized sulfation you will return the acid locked up to the electrolyte with the result being a much higher specific gravity
and rapid destruction of the plates.

personally i believe you would be far better served to follow the procedures that have been around for nearly as long as there have been lead acid batteries,
i know that it is not as sexy or new age, but it has been proven to work in cases where there is something of a battery to start with.

in any case, whatever sludge you end up with, please see a battery recycler first
to see if you could drop off the stuff with him. even then there are transport issues that you will have to attend to. legally speaking some things require special permits and placards to transport legally.
its one thing to transport your dead battery to a recycle center, but quite another to legally transport the lead based sludge in my opinion.