Consensus is that the Zone Diet works well enough if you throw in a post-WO carb up (0.5 to 1.0g/LBM) Replenishing glycogen stores is very important for a frequent, full-body routine such as this. Shoot for 0.75-1.0g/LBM of carbs.
Also the Zone Diet tends to undershoot the "mainetenance" calorie count. So, you'll want to adjust it, perhaps adding extra fat blocks for energy.
cheers,
Jules