Hi northernsole. Oh dear, I hope she is OK now.
Are you thinking of a Halti? They are good for control, but your dog will still be able to open her mouth if she has one on and she's off the lead! They only close when your dog pulls at the end of the lead-this is their purpose.
If she wanders off and puts herself at danger, you maybe need to put her on the lead during walks, for a while, and do some intensive recall training and some work around staying close to you when you're all out. It will be better for you all in the long run, her health and safety, and your heart and wallet! I am sure other ABers can guide you more on this than me (You know who you are!!!) Also consider an extendable lead so she still has plenty freedon (not ideal but perhaps better until she learns the importance of staying close, with lots of treats and praise!)
If you know your dog isn't vicious, then a full muzzle during walks only shouldn't be a problem; if people are concerned, you can explain to them that she has a tendency to scavenge. After all, I am sure her safety is your main concern.
Lisa x