I think the answers will come with your testing that day and the following.

You could do 1/2 bagel...for that breakfast with eggs and some meat of your choice.

I am testing my blood sugars in preparation for the Glumetza to start. I am finding a huge "dawn phenomenon" effect. My highest sugars are then. Then I go down the rest of the day to 120-102.
This must be why my A1C is 6.2.

Today I am 10 pts higher at every reading than yesterday. And eating mostly the same things. And I get really hungry at 4pm-6pm, so I am doing nuts then, to take the edge off.

I had a small piece of steak and one serving of lentils, and some beets (this was a very filling meal)... and today I was at 150! (no night snack).

So I've been looking up dawn phenomenon, and they say to test sugar at 2am or so to see if it is elevated. It not, then it is dawn, if it is, then something else is going on. (we eat dinner around 6:30 to 7pm).

If my "dawn continues" I will take the Glumetza at night only to start. I am to do 500mg a day, to see how the side effects are.
I'll do that for a week and see how the fastings are. I won't test so many times a day since I see a definite rhythm with my daily tests.

As far as you are concerned, don't forget the lemon juice or grapefruit...it is THAT which opens the receptors for the treat meal.

Keep your portions reasonable, and you should be okay I predict. I am suspecting this "treat day" is more for weight loss than sugar control. I'd keep the breakfast as uncarb as possible. (you have some dawn carbs already when you wake up) But try a modest carb lunch, see what happens, instead.