Great Dane - weight/behavior

Question
Hello, and thank you in advance for any information or advice you might offer.  

One of our three Great Danes, Katrina, is overweight, and despite our efforts to bring her to a more healthy weight we have failed.  

She is from rescue and was a stray so we don't have a full history.  She is approximately 7 years old and has been in our home for over 4 years.  She has been overweight since we got her, not the normal problem with rescue danes.

We exercise her daily, installed a 5 ft fence and dog door for full access outdoors and she has two dane brothers to keep her busy so I believe we are achieving an acceptable activity level or at least I hope so.

The main problem from our experience is that she is a voracious eater.  She will eat anything put in front of her and we've had to develop a feeding system to separate her from her brothers to keep her from eating theirs too.  We also have her on a weight control formula, while the boys eat lamb and rice.  When we switched the food we initially noticed a slight weight loss but that is no longer the case.  

She has always been one to eat anything, dirt, grass, tree bark, anything you can fing in the yard, yes even her own and her brothers waste material.  I believe any difference the change in food made is now just being made up for by eating more in the yard.  I don't know what to do.  

Our vets have run tests and Katrina is currently on thyroid medication but no other problems have been found.  She has a mean streak compared to my other two but that mostly shows up when there is food or treats around to be had which we try to do separately for just that reason.

Any suggestions on modifying the "she'll eat anything" behavior when outside?  or any other options to help control her weight?  

I should mention, this behavior only applies to things outside or dogfood and treats outside.  She generally does not chew things up in the house so we are lucky there.  Just worried about her health and want her to be with us as long as possible.  THANKS!

Answer
I need to know what kind of food you are feeding her first of all, how much and what brand. Also, were any tests done on her for enzymes? What does her stool look like?
Is it larger than normal, whitish or have a lot of mucous?

I need to know these things about her before I can offer any suggestions.Thanks