The ammonia in the Windex is what cleans up the haze. I've used 409 before, worked great. But that was when I first started using it.
I have posted my process before and I it has always yielded me with zero haze issues.
You need to keep the buckets of water clean. I use a three bucket system.
1) Get the tile damp but not wet
2) I use my hand palming the grout into the joint. This eliminates much of what is dragged across the tile leaving the majority of the haze.
3) Then use a white scrubby or scrubby sponge. I like the white scubbies that are typically used in epoxy installations. These sponges lift a good majority of the grout off of the tile.
4) Then I use a standard sponge in separate bucket. I wipe it on one side, overlap by half and use the other side of the sponge to wipe. It's rinsed and repeat. That bucket is changed about every 20 wipes.
5) The next pass is with a microfiber clothe (or sponge). I fold the clothe twice to give me 8 separate sides to use. I will wipe it down with one side, flip, wipe, unfold wipe, flip wipe until I have used the entire clothe. It's rinsed and I wipe again. This bucket is changed every 10 or so clothes
6) I now use a dry microfiber to dry the tile and pick up any stragglers. This clothe will eventually get wet enough to be useless as a drying clothe, so it goes into the wet bucket after 20 or so wipes.
The buckets are rotated. So the microfiber bucket becomes the sponge bucket and the sponge bucket becomes the scrubby bucket.
It's a lot of work, but it works. I usually have two or three guys working with us when we are installing. One guy's sole job is to switch out the buckets.
Hopefully that helps.
Rob