From your description, it sounds like you will have 3 sources with common BICK & LRCK. This will take 5 DAI lines. If the other two sources are completely independent, they will take 3 DAI lines each (BICK, LRCK & DR).
This means you are using 11 out of 20 DAI lines. You have 8 SPORTs available so that is fine. You may want to sync with the ASRCs.
You have two SPI ports available so that should be fine as well.
From what you have written, you are good to go .
Al Clark
www.danvillesignal.com