Your Nacho clearly is not familiar with Amels - by all means, fasten the bimini frame to the shrouds and do not clutter it with vertical members going to the deck.
Look at the connection of your balooner "wishbone" stabilizing bar on the main mast shrouds for a model of how to do this. (Commercial clamps are also available.)
If you search the photos section for "Sangaris" you will find an album of how mine is done, with only four connections to the mizzen stays. (Or just click this link: Sangaris
No connection needed to the Mizzen. Bullet-proof and clean.
I've done mine in "T"-Top style as I did not want full enclosure but (hopefully) Nacho can easily close yours in.
Btw, using the same 25mm tube as the rails will give you plenty of strength plus a complimentary appearance.
-- good luck with your project.
Craig - SN68 Sangaris, Tropic Isle Harbor, FL