Did you know there are baby wearing groups all over the country? I found one in my town. I went with my baby to one of their meetings and they were great. They had a bunch of carriers to try out, and they taught me how to do the moby properly.
If your location is correct, Tampa isn't too far and they appear to have a big active group: https://m.facebook.com/TampaBayBabywearing/. If you are not near Tampa, google babywearing and your location.
It was like Le Leche League for baby wearing :). My group even had a lending library so I could borrow different types of wraps for a month to try them out before buying. Look for a group in your area.
ETA: It is a lot easier to troubleshoot in person, but over the internet, my best advice is this - are you doing the hug hold or the kangaroo? If you are doing the hug hold, maybe try the kangaroo (google to know what I mean). When you do the moby in the kangaroo hold, the material in the front middle should be under the baby's bum only, not his feet. That's what supports his weight. You tuck the feet under the side wraps gently to keep him from wobbling, but his weight should not be on his feet. The stretchiness of the fabric shouldn't matter - I made my own moby-type wraps out of material that had very little stretch at all.
For the head support: as comfortable as I was wearing my baby, and I did it all the time, I always kind-of kept one hand on them. I would take it off for a minute or two when I needed both hands. But it was some kind of basic instinct to have a physical hand on the baby even though all the weight was supported by the wrap. So when tiny, my hand helped steady any head wobble. And once he was bigger, he had enough neck strength that I didn't worry about it. Also, for safety reasons, your baby's head should NEVER be at an angle or fully covered by the wrap. Your baby's head should be in the center of your chest above your breasts. If he's in the right place, you should be able to kiss the top of his head by simply bending your neck.
ETAA: I also used and loved ring slings and my Snugli carrier. Find a group and try them all!