All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
It is permissible for you to re-use the water that was used for ablution in what you mentioned as there is no Sharee'ah text that prohibits it. In principle, all things are permissible and this principle cannot be overruled except with evidence.
The jurists speak about the water that was already used in ablution regarding the ruling on re-using it in removing the state of ritual impurity [whether for Ghusl or ablution], so some of them prohibit this while some others permit it.
In any case, re-using this water for cleaning (flushing) the toilets is permissible.
Indeed, we encourage you to design this system as this would be very beneficial; may Allaah help you and facilitate for you this matter.
Allaah Knows best.