Hi!

I'm sorry I misunderstood you earlier!
It sounds to me like you are doing low-carb BFL with a "free day" on Saturday, which you use to carb up. Well, in that case, it sounds to me like your cardio plan is great. Spinning class is an awesome high-intensity workout, so I don't see why you would have any problems doing this.

Keep in mind, though, that you do not want to do your weights on the same day as your cardio. Nor do you want to do two intense cardio sessions on the same day.
Hussman's Workout Advice

I don't think that Hussman's concerns about glycogen depletion apply to us, who are on LC diets, but I would think that his advice about ATP and creatine phosphate stores would apply equally well to us. If I'm mistaken about this, I'm sure someone here will correct me.

It sounds like you have a really solid plan. Good luck!

Trilbe