So a couple of things. One I’m not a nutritionist, but it’s always easier to comment on other’s training than your own. I’ve tried what you are referring to with “cheat” meals a number of years ago. It kind of “worked” but is not a healthy way to handle weight loss. By doing a cheat day like this you’re teaching your body to pack away those calories as fat because it doesn’t know when it is going to get the next day when you’re not under eating. It also creates a reward mechanism of if you do your training you get a reward to eat huge amounts of food. That is not a good cycle to get in to.
So I would stop doing that cheat day type of cycle.
To answer the other questions: Yes I’ve increased my fitness while losing weight. It takes fueling at the appropriate time of day for the training you’re doing and NOT eating extra on other days or times of the day to make up calories. I utilize the kJ’s burned calculated by the power meter data to add to my BMR plus a basic level of activity for the type of office work I do. For me if I don’t exercise that is around 2,000 calories per day. If I ride that is usually another 750-1000 calories during the week and can be a lot more on the weekends during nice weather when I’ll ride 3-5 hours each day.
Bottom line is eat healthy all of the meals of the day and fuel with 250-300 calories per hour when riding. When you do this you’ll get off the bike not feeling like you need to eat an entire pizza. Then if you’re wanting to lose weight get about a 400 calorie deficit per day but don’t get that deficit by reducing the amount you eat surrounding exercise. Do it by reducing from breakfast, lunch, or dinner. And then don’t do the cheat meals. That is what I would do in your case. The amount of performance improvement by fueling correctly immediately before, during, and after training sessions is huge.
Just my two cents as someone who isn’t naturally a tremendously skinny person. More of an athletic build like a basketball player rather than a cyclist.