Welcome, kamakiri, and good luck with your new kanji endeavor ;-)
I'd like to add my two cents, even if some of the following things have already been addressed by other users.
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EDIT - TL;DR:
1) Forget everything you think you know about kanji.
2) Then read the last part of this message (key points of Heisig's method).
3) Finally, re-read the book's introduction and skim through the start of each chapter, to get a better grasp of the method.
4) Give the SRS integrated into the site a try, as PotbellyPig said.
Sorry for the long post. I got out of control as usual

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First, it happened the same to me with Anki: it was too cumbersome for me at the beginning, so I used (and still use) the SRS integrated into the site and it worked beautifully well for the 3030 kanji I'm able to write now ;-).
At some point in the near future I'll migrate to Anki for the sake of unification and simplicity, as I'm already using it for vocabulary; it has some advantages too (like being able to review off-line or to add kanji outside those 3030, to name a few), but I'm really grateful for the SRS implemented by Fabrice. Don't be shy to give it a try if you are not ready for Anki yet ;-).
Second, I don't know how much kanji you know at present, but I have to recommend you to FORGET ABOUT EVERYTHING you know about them -well, more realistically, to pretend you forgot- before you start with Heisig's method (and please note that I'm being flexible about what "knowing a kanji" really is, as it can mean any combination of the following: being able to write it, able to recognize it, able to read/pronounce it, knowing some vocabulary words associated to it, etc).
So: forget about readings. Forget the vocabulary. Forget about radicals -if you already know enough about them, which I guess it's the case-. The reason I'm telling you this is because Heisig's method -taking into account you've been playing with the language for some time now (to the point you're teaching it!)- is granted to blow your mind up in several ways, so IMHO it's better if you abandon any preconceptions.
Having done so, now it's a good time to re-read the introduction of RTK1, which is more dense and has more information than it might seem at first, and then, always in my humble opinion, it would be a good exercise to go through the entire book to skim over all the bits of information at the start of every chapter and get a grasp of what this thing is all about. Some of your questions will be answered (for instance, yes, you are supposed to do the reviews going from keyword -front- to kanji -back- drawing it -even with your finger in your hand- before checking the answer). Anyway, let me try to break the method down and put it all together in the next paragraphs:
The main idea behind all of this is efficiency. The method is designed to require from you the least amount of time and effort to tame THE WHOLE ISSUE of kanji. Sadly, that still means you'll invest lots of time and effort, but it'll be a tiny fraction compared to other methodologies; in my case, it's the only method that even worked beyond the 50 kanji mark.
What this
efficient approach means is you'll be doing awkward things because your goal is a long term one and you'll be taking the shortest path there. Put another way, you'll be taking an amazing shorcut, but doing so you won't be able to get any short term achievements or put all of your knowledge to much practical use until you get, say, around 80% of the way (of course this last statement is very subjective and controversial, based exclusively on my personal impressions, not on any real data). It may sound strange to proceed like this but based on my experience I can only say it's the most clever way to tackle this problem, and hopefully you'll see its advantages once you give it a try. Given that some of the users can go through the whole first book in a couple of months, and a majority of us does so in a period ranging from 4 months to a year (actually, it took me more than two years, but I'm kind of an edge case for multiple reasons), it doesn't seem like a bad choice, does it? After all, you'll be able to differentiate and write appropriately more than two thousand kanji after that period (even if you didn't learn any real vocabulary during that time... but how hard will it be to learn vocabulary using kanji after that? ;-).
Having established all of the above, let's analyze the methodology: think about the phrase "divide and conquer". The first part of the series, the RTK1 book, is probably the most useful (a lot of the users here would agree with me on this, I think), but here comes the biggest mind blow you'll suffer: as already stated, with it you'll learn to write every single kanji in the 常用 ("Jōyō") list (give or take) without ever learning a reading for them or a single Japanese word. I wish I had the words to explain how this is so much the right thing to do but, apart from what I explained above, you'll have to just trust me. Then, the second book (RTK2) is about learning the readings,
only when you've already finished the first one. Finally, the third book (RTK3) is just a repetition of books 1 and 2 (it has two separate parts for this) for additional kanji, up to ~3000.
I didn't like the approach of the second book, and reading this forum you'll get to know that a lot of users felt like me, while a few found it really useful (the rest of us just jumped straight into vocabulary without caring much for singular readings, you'll find more information diving into the forum). Still, even if it's not for everyone, I think RTK2 has its merits.
As this message is already too long, let me finish highlighting the main points of the method for the first part (RTK1: writing and meaning), which I think remark the best of Heisig's ideas and his ingenuity:
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RTK1 key points
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1) You'll learn just how to write the kanji (which will enable you to recognize them as well) but not to read them nor any vocabulary formed with them (divide and conquer: now you're just becoming friends; reading and vocabulary is for the next stage, in which they already form part of yourself :-P... so forget about readings and vocabulary in your reviews, for the moment).
2) You'll associate a "meaning" with every kanji (although kanji don't really have a "true" meaning: some of them represent a very concrete concept -or several related concrete concepts [sun, day]-, some other cover diffuse or vague areas, and some even have several incoherent "meanings"). You'll be doing so (associate meanings) through the use of keywords (which are just "mnemonic placeholders"; at a later stage, while learning vocabulary you'll get to know them better and substitute this placeholders with a deeper rooted concept, not relying anymore on such keywords, so don't worry too much if they aren't extremely precise: the more precise the better, but it isn't critical, really).
3) You won't learn them in the "most useful" order from a
practical usage point of view, but on the "most efficient" order
to learn them all (this allows you to be *several times* faster).
4) As if the previous ideas (which include the systematization of the order in which you learn the kanji) weren't revolutionary enough, he also systematized the whole mnemonic method: he unraveled the kanji with more precision than radicals do (admittedly this is not so revolutionary) and assigned each part a VISUAL counterpart to be used when making a VISUAL story, which serves as a way to relate all the parts of each kanji with its keyword (and sometimes their placement within, too, when necessary). Think of it as a "visual glossary" [Note: I'm clearly abusing the term "visual" here, but for good reason: the stories have to be "visualized"; it's not enough to just learn them as if they were a series of words -I have some exceptions to this rule, but not more than 20 ~ 50 in my whole collection of 3030 stories-; it's very easy to overlook this at the beginning and it will come to bite you later].
As a final note, the stories, too, evolve with time: at first you have to construct them very detailed, but with every review they slowly fade away until only the key points of it remain; finally, you no longer need the story at all and go directly from keyword to shape... but sometimes, when your mind is unable to recall that direct link, the story is still there and comes to your rescue.
I hope this long digression served to clarify things a little.