It sounds like, if she's so obviously overweight, has hard 'fat pads', she is not just overweight but obese. And very likely insulin resistant/EMS. I don't get why on earth you're feeding her ANY grain or alfalfa at all?? Those are both high energy/calorie feeds, and grain is also high sugar/starch, which will be contributing greatly to metabolic issues! No, if she's overweight, you don't need to replace those things with anything, except for literally a single handful of beet pulp or alfalfa pellets moistened, to mix any nutritional supps with.
I'd definitely be giving her extra magnesium, along with whatever else she may need. Magnesium has been shown to be deficient in most diets anyway, and when horses(or people) are on high carb diets, more magnesium is used, so needed. And when an animal(or person) is in stress, particularly chronic, including systemic stress, such as IR/diabetes, they use/need more too. Magnesium has been shown in people, to help 'reset' the metabolism, resensitise the body to insulin in type 2 diabetes. From that research we have found the same is true for horses. So... look into it & it's one mineral that's worth adding on top of a 'well balanced diet', especially for a horse like yours.
Not sure about your hay - depends a lot on how it's grown/cut, as well as what type, but if you get a regular/big supply, I'd say it's worth testing, to see if it's low NSC. If it's not, or you're not sure, I'd be soaking & draining it before feeding, to leech out some of the sugars. If your pasture is overgrazed/stressed, this will be higher in sugar than healthy grass. It doesn't matter how lush it is(water content), but how rich it is, and stressed, overgrazed grass can be quite concentrated.
Exercise, as with people, is another important way of losing weight & getting healthy. I'd be taking her out a couple of times a day for a long walk with a fair bit of trotting too, as she can handle without getting too pooped.