Yes, you are over thinking this. During this phase, the first month or so, there is virtually zero correlation between your loss rate and what you are doing, as there is a lot going on with your body changing states trying to adapt to this big caloric deficit that you have thrown at it. Do a search here for the three (or third) week stall and you will see lots of anxiety over what is my weight loss doing and what have I done? Your loss will slow, often stall and maybe climb a bit before going down again. It often happens right around the time that our diets are moving from one stage to the next, so "that mush be it!" but it isn't - even those of us who never had all those stages go through something like this.
Short answer is that when you go into a serious caloric deficit like this, your body first starts drawing on you glycogen reserves, short term carb reserves stored in you liver and muscles, which give you your quick response bursts of energy. There is a lot of water weight associated with glycogen. Once that is largely consumed, your body usually pauses to see if you are really serious about this caloric deficit thing. Then it will start to draw on your fat stores, which is what we are here to do in the first place. Fat also burns more slowly than glycogen/carbs (its that 9 cal/gm vs 4 cal/gm thing,) and it has to rebuild some of your glycogen reserves again (water weight on) so weight can be real flaky here for a while.
If you really feel that you aren't eating enough, then a bit more wouldn't hurt and may be helpful, though that won't be what gets your loss moving again. I was up around 1100 calories fairly quickly, within the first couple of weeks, but I was also progressing on food types more quickly than your program suggests, and we had no specific caloric guidance. Others on these forums at that time were insisting that anything more than 6-800 calories would be death to your weight loss. I did fine, at least with my decent guy metabolism, and they did fine as well. I wouldn't rush things on too much, as it is much easier to add more later if you feel the need to than to cut back once you get used to eating a certain amount. I didn't increase my average calories from there until I was within about 10 lb of goal weight (at about six months) and needed to slow things down.