BIWI's bootcamp and what you describe as an initial low level of carbs to get into ketosis are actually very similar - the only difference with bootcamp is that you don't have to weigh stuff if you don't want to as you are restricted to foods that are naturally very low carb anyway, though getting an idea of the number of carbs in your regular portion of e.g. broccoli is not necessarily a bad idea.
low carbing is not just about keeping your carbs low, it's also about where those carbs come from. you could eat nothing but roasted macadamia nuts and/or highly processed atkins chocolate bars and technically remain under 20g carbs, but that would not be healthy, and from your post that's not what you would want to be doing anyway. so following bootcamp initially, while counting carbs at the same time if you find that easier, would probably be what you would be doing anyway and it would at least give you some guidance as to what food choices to make if you need it. do just be a bit careful if you use something like myfitnesspal to track carbs though, as often the food entries can be a bit dodgy accuracy-wise, and on american nutrition labels the carbs are listed differently (they include fibre in the carb count, which would then be subtracted, but on UK packaging the fibre is already discounted).
you're right that the aim is to get into and stay in ketosis, and i think that the reason for starting with a very low level such as 20g carbs is that this is pretty much guaranteed to get most people into ketosis unless they are really severely insulin resistant. after the initial two weeks or so of getting used to the new way of eating (WOE), and getting over any 'carb flu' withdrawal symptoms you might experience, you can start including a wider variety of foods - perhaps a few (not too many) berries, nuts, small amounts of carbier veg (like carrots, not sweet potatoes), still NO grains, sugar etc - with, as you say, the aim of remaining in ketosis and continuing to lose weight. not everyone does this (some prefer to stay stricter for longer, and you do really need to watch portion sizes). because everyone is different, some people will tolerate higher levels of carbs while still remaining in ketosis and losing weight than others. it's about listening to your body and finding out what suits it best. some people find that dairy, while usually low carb (except milk), can stop them losing weight if they have more than a certain amount.
if you read atkins, then once the goal weight has been reached, you can again start to increase carb levels until weight is stable. again, starting with increasing the levels of carbier veg is a good idea, rather than going straight to eating bread. as with any diet, if you go back to your previous way of eating you will put the weight back on.
although this way of eating is not very forgiving if you eat something very high carb (you will replenish your previously depleted glycogen stores, which can make you appear to have put several pounds on overnight - you wouldn't be putting on that much actual body fat in one go), you can as you say eat much more than you would be able to with other ways of eating, and the food is so satisfying and your blood sugar levels so much more stable that you feel fantastic and full of energy.
even if you don't want to do formal bootcamp, do feel free to come and hang out on the ongoing threads as there's tons of support and knowledgeable people. although the foods you can eat are varied and delicious, it can be hard eating in a way that is contrary to what people have been taught over recent years. you're definitely doing the right thing by reading up on it - it's important to understand why you need to make certain food choices over others.
hope this helps!