Your body is larger than the sword, so it cannot cover all of it. None the less, cover as much as you can without awkwardness.
Fabris is against standing up straight. He claims it is slower at offense and disunites the body and the sword.
It is better to carry your body forward, but if you cannot then stand up straight. If you force a position you will be unable to move quickly.
You should be comfortable and mobile when bent at the waist. If you can keep low in such a manner, you will be stronger and faster. Since you present a smaller target, your sword has to move less to defend you.
You need to practice holding your body low, it won’t come automatically. With practice you will be quicker, more comfortable, and safer. You can attack from a farther distance and those attacks will involve smaller movements. Attacking from a backwards angle, e.g. Capo Ferro, to a fully extended lunge is a really long action.
Make sure your weight is not on the foot that has to move next. If it is, it will cost you two tempi to move.
Your head is actually safer because it is behind your forte.
This stance will by tiring in practice, but the benefits are worth it.