Shedding fat is going to come mostly from diet.
For training, find something you can consistently maintain and keep at it. It seems like you have that. Just make sure you are working hard and giving it your all. I don't think you should entirely neglect heavy training. I would consider including some heavier sets from time to time.
OK, the diet. You asked for an honest response, so here goes, a Cheat Day is entirely excessive. And I respect that you said "I must have a cheat or I WILL binge." But honestly, why do you look at eating healthy as deprivation? You can still eat delicious foods. Get creative with spices, vegetables, etc to add variety and flavor to meals.
I believe you need a shift in perspective, rather than viewing a healthy diet as deprivation, why don't you try to view being overweight as deprivation. While you are overweight, you are depriving yourself, your family, your friends, of a healthier, more active version of yourself. Hopefully, that will help motivate yourself to endure with a healthy diet.
If your weight has been stable and your training and diet consistent, then it is time to start reducing some calories, likely in the form of carbs or some fat. Just lower enough to re-start weight loss, maybe 200 calories at a time. Re-assess weekly; is the scale dropping? Are you seeing improvements in the mirror? Are your measurements decreasing (if you are measuring)?
If you are planning a cheat, then make it a meal only, not a full day. And make yourself earn it. For example, it you are planning on having a cheat dinner, than consciously eat slightly less than normal for your earlier meals of the day and also train harder that day. That will help compensate for the additional calories.
James 1:16-17 ESV
Do not be deceived, my beloved brothers. Every good gift and every perfect gift is from above, coming down from the Father of lights
With God's help...Mens sana in corpore sano