<p>Does anyone have any experience with a tool that generates test strings from a BNF grammar that could then be fed into a unit test?</p>

I don't have an answer to the tool question, but I will say it is fairly easy in any text processing language (perl/python/etc) to randomly generate sentences from a BNF grammar, and slightly more verbose in a bigger language (Java/C/etc), but it shouldn't be too hard to roll your own.
The problem with this, of course, is that it can only generate strings in the grammar, and unless your grammar is very simple, the test space is infinitely large.