This might be a dumb idea (I have absolutely no experience), but they make this two-part putty like epoxy used to seal pool leaks like around a return. I am led to believe some varieties can harden underwater.
So, could you get some of this, mix in some sand, and spread it in a strip, probably along the front edge of the steps?
I admit this suggestion isn't well thought out, and easily could be a really stupid (or worse, dangerous) thing to do, but....