He won't be upside down with his head opposite the rings, it just seems that way. His head will rest against the upper edge of the outer rail. You can fold the fabric back, making a double layer to support his head, and that works nicely. I also second the rec of trying the upright snuggle hold.
As far as technical use of the Maya Wrap for best performance and comfort, here's my standard list of suggestions:
1. Make sure the shoulder flap is open BEFORE you thread your sling. That means that if you wear your sling on the right shoulder, the edge of the open flap should be the bottom edge of your sling all the way around. If you wear it on the right, it should be the top edge all the way around. Otherwise, the body of the sling WILL be twisted, and twisted is not good.
2. Once the sling is threaded, find the outer edges of the fabric in the tail and pull them away from each other. You want the edges of the fabric to be the edges of the tail. The pocket will be on the front of the tail (facing out). That way when you need to adjust, you know the inner edge of the tail controls the top rail of the sling, and the outer edge of the tail controls the bottom rail.
3. Have the sling adjusted close to where you want it before you put the baby in, so that you mainly adjust the edges of the tail. Otherwise, you start with the baby really low and will likely pull the rings down instead of pulling the baby up.
4. Make sure the lowest point of the baby is no lower than your waist. If the baby is in a hip or T2T carry with feet out, make sure the fabric comes into the back of baby's knee so the thigh is up in a seated position, parallel to the floor, and the top edge is at least up to the armpits. The baby's butt should be slightly lower than the knees so they are really sitting down in the seat created by the fabric.