Tell us about yourself!
I would not expect a simple filter to remove any toxins, however I would expect it to remove particulates. That should prevent clogging of the system, and removing toxins post sprouting may be as simple as rinsing. I'll leave that up to you, and Google to figure out ;) Even if the phytic acid remains, it's still going to be (way) better to sprout than for someone to continue eating a standard american diet. Don't let that slow you down in the least, it's always better to do something than nothing. Post it when you're done, I'm sure there are others who would love to see the potential for deviation from the original project. Happy sprouting!
I suspect your proposed setup will work, but you may be reducing some of the health benefits of sprouting. One thing that occurs during sprouting is the removal of Phytic Acid (and possibly other toxins/undesirables), which then is discarded in the used water. As you can probably extrapolate, you will then be re-washing with Phytic Acid. If there is no option for fresh water, perhaps just a larger storage vessel to significantly dilute these elements. Exchanging the water would also help alleviate this problem. I'd like to add that I am not a botanist, nor do I have any other official credentials to make these statements. I am simply a health nutrition enthusiast. This answer is true to the best of my knowledge, and according to things I have read in my experience.
1 crate, two bricks, some binding wire, a piece of bamboo and some string. Thread the string outside of the crate so it has the correct direction of pull on the stick then drop it in through the top, and bait it.
Food of the Future: Window DIY Spirulina Superfood