All of the issues you have mentioned certainly point towards a grain "allergy". Grains are essentially grass seeds and are generally used as fillers, but are totally unnecessary in a dogs diet. This can be further seen by the larger output of undigested material.
Protein percentages in foods are a little misleading, since you feed far less of these foods, sontge grammes of protein consumed per day is only slightly greater,but the protein quality is better (animal not plant)
Since skin and fur is essentially protein you can see why more high quality protein will help, the body uses nutrients for core functions (heart, lungs brain etc) first and only when there is sufficient left after these core functions are satisfied does that surplus go to help repair the skin and fur.
Anal gland problems are often due to soft stools, another side effect of grains for many dogs, though there can be other causes. Firmer stools help to express the glands daily and stop them getting blocked and infected.
Finally weight, excess carbs tend to be laid down as fat, and you have to feed excess carbs with many foods to get sufficient levels of other nutrients like protein and fat. So by feeding appropriate amounts of a low carb (high protein) food the weigh issue can be easily resolved.
As already mentioned, take 2 or 3 weeks to switch over, start with a conservative amount of food, you can always add a little more once the excess weight is coming off,
Good luck with your decision, I'm sure it will resolve the issues.