Mayb try some hypo on it, but to me, it looks like theres a fair bit of carbon and stuff on there aswell. We used to use hydrofluoric acid to get that off the bricks, but it damages stone.
Try tensid.co.uk
they do all kinda of chems for all kinda of different applications. They have helped me out on a number of tough jobs. Im sure if you email them a pic, they will send you some samples of stuff they think will do the job.
otherwise you COULD try a small half a stone brick with hydrofluoric acid. Depending on where you are, it might be difficult to get. tensid sell it as heavy duty restoration cleaner.
Just do as many test with as many different things as you can.. and one with plain water, so you can compare. if the plain water brings it up almost as good as chems, just save yourself the hassle and use plain water.
Im sure someone else will be along soon to give you a better solution..
looks like a good job..