Why only "a bit"? There's 2600 calories in a gallon of whole milk alone, which was what I was drinking in addition to eating about 3000 more calories a day when I decided I was tired of being 170lbs a few years ago. Even then it took me almost two months to gain 30lbs.
Give this a look
(WFS aside from some language) for when you're ready to adjust things after this 30 day experiment is over with.
Going low carb while training intensely is a good way to jack up your metabolism and other systems. I've had a few phone consultations with a naturopathic doctor after doing an adrenal stress index test, and he said about 90% of his patients recently have been CFers who have developed difficulties regulating blood sugar and insulin levels from undereating while on VLC diets. It may work for some people, but if you're feeling like crap while doing it that's a pretty clear sign something is wrong.