What opening is suitable to defend the stonewall?

Possibly helpful:
Grandmaster Repertoire 11: Beating 1 d4 Sidelines by Boris Avrukh (2012)
https://web.archive.org/web/20140627001415/http://www.chesscafe.com/text/hansen164.pdf
http://www.qualitychess.co.uk/ebooks/GM11-1d4Sidelines-excerpt.pdf
Dealing with d4 Deviations by John Cox (2005)
https://web.archive.org/web/20140627032909/http://www.chesscafe.com/text/hansen89.pdf

I like to approach it in a sort of accelerated gurgindize set up...kside fianchetto (but I often wait on bg7), Bg4, h5, Nh6-nf5

I agree with FunnyAnimatorJimTV, especially the portion about mirror moves. However I also would like to add, that in the Stonewall, white usually has troubles with one of their bishops - avoid white trading off the bad Bishop in itself causes white troubles. Lastly, an aggressive response that works well against the Stonewall is to simply develop, then castle long (O-O-O). This makes the Stonewall surprisingly tougher for white. Stonewall as an opening is a solid, heavy theory, opening that should definitely be taken seriously. However, for reasons that I have mentioned (and others) this opening (like the Tarrasch Defense) seems to only be popular until about 2000 Elo. However, it is often seen at club levels - sometimes also serving as a surprise weapon for white.
With this advice, I hope you will like facing the Stonewall as much as I do. Just stay alert, not underestimating this opening, as many players find this "wall" hard to break once setup. Lastly, if you really want to invest into countering the Stonewall: look into forming a blockade on key pawns. This last tip can be a great asset, but requires knowledge a lot deeper than a forum response would allow (and honestly likely includes knowledge that I do not yet have, although I have heard that some titled players use this blockade strategy versus the Stonewall). Best of luck breaking this "wall" that was intended to prevent attacking schemes from success.