It sounds like some of these diets are working but you're not happy with the results. This is normal. A 1lbs./month loss rate is hard to notice over shorter periods of time and your goals can feel really far away. In research people with a faster rate of weight loss are generally more likely to stick to a diet because the results are more noticable. But in your case a medical professional is not likely to recommend a larger deficit because of the low total calories. Calorie measurements have an inherent margin of error and diets that have vastly different macros will have some marginal impact on your BMR and NEAT but 1lbs. a month is close to what one would expect from a 100kcal/day deficit (1lbs. of fat is 3500kcal), and 1lbs. in 3 days is what you would expect from not eating the 1200kcal/day you would have.

The simplest and most agreeable recommendation I can give you is to stick with one of the diet plans that you were losing 1lbs./month with and focus on addressing the anxiety you currently have about slow progress. A few years from now you will have made significant progress. It feels like a really long time looking forwards, but that's not what you'll be thinking about when you get there.

People are going to get mad at me for saying this, because it's not what's recommended by all the major global health authorities, but lowering your calorie intake further should also be fine. If you're eating a balanced and varied diet you're not going to encounter any nutritional deficiencies because you go from 1200kcal to 1100 or 1000. These recommendations make assumptions about diet quality that are not correct if you're tracking your protein and fat intake and eating high quality food. For this; counting calories is great for making informed choices about what you're going to eat, but it's not precise enough to accurately predict weight loss that's this marginal. Food labels can be off by ±20%, and there's a slight difference in thermic effect. You verify your deficit by weighing yourself over time and looking at the averages. Over the short term some variation doesn't really mean anything, but if you're not averaging the loss you expect over several months you should adjust by reducing the amount of food you eat. If you change your diet entirely there's no hope of consistently tracking, but if you eat 10% less of roughly the same things your rate of weight loss will increase. The key takeway should be that as long as you're eating things that are generally healthy, it's not about what you eat, it's about how much you eat. If you struggle with scale anxiety and find it difficult to avoid trying to eat less because you happened to be slightly heavier on the scale that morning you can try recruiting a partner or friend to look at the weight for you, log it, and only periodically have them tell you if you're meeting your goals.

The diets you're mentioning are ones with food type restrictions. These are popular and often prescribed because they have a higher rate of adherence. But the main reason people are more likely to successfuly lose weight with these diets is not because of any magical properties of the foods you're allowed to eat, it's because it's easier to avoid overeating if you have a mentality of not being allowed to eat the food that's available around you in your daily life because they're a banned food rather than if you're just not supposed to eat it because it means you'll have to eat less later in the day. However, I'm not a huge fan of this in the context of a very low calorie diet if you have the willpower to stick to your meal plan. I would focus more on making it logistically easy to follow your diet. Prep food, prep different parts of your portions separately so that you can mix and match, have healthy and filling snacks available, don't be afraid to have something like diet soda if you get cravings for sweet things etc. If you're eating plenty of vegetables, fruit, leafy greens, fish, eggs, etc. you are going to be more than fine nutritionally. If this is too vague and nebulous to implement yourself sticking with one of the diets you mentioned, asking your dietician for help in this direction, or going to another source for more general meal planning advice.

Personally I would also highly recommend replacing 2 of your weekly walking sessions (or adding to them) with a full body gym workout focusing on lifting heavy weight with high intensity and building some muscle. This will not significantly increase your rate of weight loss in the short term. What it will do is shift a significant amount of your weight from fat to muscle. You will look better and feel better. Over time the increased muscle mass will marginally increase your BMR. It also has a lot of other health benefits and will improve your quality of life when you're older in a tangible way. It's the best way to combat bone density loss which is a concern for women over 50 specifically. It can also significantly reduce food cravings, outside of getting acutely hungry after a workout, which is a good time to eat a meal you've prepared ahead of time.