I vote for the strap.  Personally, I always play with a strap, and it no doubt helps keep the guitar in position and therefore mitigates the need for arms to control the instrument's position and movement.  

Fingering notes and chords without looking at the neck is a standard, and desirable goal.  You can try exercises in which you bounce back and forth making chords... over and over again without looking until the muscle memory sets in.  If that doesn't float your boat, try using a mirror.  You can find relatively inexpensive narrow 4' tall mirrors at the discount stores (mine came from Walmart).  Set it up in front of you and look at it rather than the guitar neck.  That should keep your head up.

Good luck and keep playing.