I sympathize, Sarah. I used to think I was pear shaped and whether I was or not, I definitely put on weight on my hips and thighs as a younger woman. Now when I gain, it goes to my mid-section first and then all over the rest of me. These days, my waist is an inch bigger than it was when I was 20. And yet my scale weight and overall body fat percentage is actually lower now than it was then!! In other words, some change is probably inevitable, even if you are fit and in perfect health.
I have bored everyone often enough with my own story, so I'll try to be brief. (Ha!) I lost 35 pounds in the midst of menopause and have kept the weight off (give or take a couple of pounds in either direction) through a combination of a fairly but not obsessively clean diet (mostly vegetables, lean protein, healthy fats, whole foods -- with treats of various kinds in moderation.)
I try to avoid white flour and highly processed foods as much as possible, but again, once in a while seems to be fine for me. I don't eat a lot of added sugars but do indulge in a square or two of dark chocolate on most days, and I eat a fair bit of fruit.
Generally, I aim to keep 80% of my meals "clean," but in fact, I tend to focus more on adding healthy options in vs. taking stuff away. For example, I concentrate on eating more veggies rather than less of something else -- and eating less of the other stuff takes care of itself if I am full of veggies!
I try to exercise five to six days a week between 30 minutes to 1.5 hours (depending what I'm doing). I think lifting weights is the best for revving up your metabolism. I aim to lift at least twice a week (though I don't always achieve that) and I do crossfit a couple of times a week as well. As Mo said, it's important to challenge the body by doing different things and this will help with weight loss and muscle development.
Body weight workouts (like those you describe) can be great, but in many fitness classes, people are quite simply, not challenged enough to make it truly valuable apart from cardio benefits. I know that for me, my body composition changed dramatically from lifting weights, in a way that it never did when I was doing mainly cardio and isometric workouts.
Another helpful strategy is interval training. This, in combination with resistance training, seems to lead to the greatest fat loss for most people.
I also do a lot of walking, jogging, yoga, hiking, skating, etc. Depending on weather and what's going on.
Laurinda makes an excellent point. There is no one size fits all prescription. Sometimes we have to self-experiment a bit. One person's body type and metabolism will be different from the next person's. I'm a sort of ecto-mesomorphic body type...I can probably eat more than some women my height without gaining. But I can't eat the way my super ectomorphic husband eats. Alas.
As Laurinda also said, it's important, if you try something, to try it for long enough and to monitor so you can see whether or not you are actually getting results.
I found it was helpful to get some coaching, but I needed to lose a lot more weight than you do. In your case, it might be a question of switching up your exercise routine. But you shouldn't have to starve yourself to lose weight; it is possible, in fact, to eat too little -- and nothing slows the metabolism down like extreme dieting.
Good luck with this - I know it can feel oh so frustrating, but I think you are doing a lot better than I did. At least you are acknowledging the problem. I just tried to ignore it until I literally had nothing to wear because I couldn't even fit into my yoga pants any more!!! ;-/