Got this one via email...
I'm glad that you've found success in leaning out!
Good questions. First, you should realize that cautious increases in kcal after a diet is not the brainchild of mine or John's. And use caution implementing any diet regime, as most public/ commercial ones are kind of "at the hypothesis stage" (as yet unproven), okay? I'm glad you're reading a lot; check out those references on Medline and pan to the bottom of the abstracts for conclusions, if you're comfortable doing so.
I can tell you this, if I were personally consuming just 1300 kcal for a long time, I'd be very cautious for the first 6 weeks or so. (For the reasons I outlined in the yo-yo dieting article.) The metabolism can be pretty crushed (leptin and thyroid depression, etc.) and fat cells can be in a "needy and greedy" state.
Without obsessing over minutia, a 300-500 kcal jump in daily energy balance (not just more eating per se) would not be unreasonable. It could be done by cutting out a cardio session OR adding a tablespoon of medium chain triglycerides & a tablespoon of safflower oil to an additional protein shake. (Depends on how much protein is already in the diet; >200-250g daily is already a LOT.) I'd also use caution with added fat during the sensitive post-diet period but 2 Tbsp. isn't much. (Note: small amounts of specialty fats like CLA and EPA+DHA from fish oil might also help reduce negative consequences of calorie swings.*)