Disclaimer before I say anything else: I’m a Chinese speaker, so kanji are rarely a problem for me, and I also don’t struggle to pick up new readings or meanings unless they’re obscure. As such, I don’t use any SRS at all. It seems that this doesn’t apply to all Chinese speakers, seeing as there are Chinese speakers among WK users, and the least we can say is that some of them like the structure that WK provides even if they would be fine studying kanji usage in Japanese on their own. Furthermore, this means that what I find helpful may also not apply to you. Nonetheless, I’d like to offer my experience.
First of all, as almost everyone has said so far, it’s quite normal to be unable to speak or write naturally in the beginning. This is true for any new language. You need to reach a certain critical mass before you’re able to form anything other than the simplest sentences, and unlike a young native speaker, you probably don’t have a helpful adult near you to answer your questions in real time. You’ll need to learn a few more words and absorb a few more structures before you’ll finally be able to make sentences of your own, so your expressive ability should gradually improve as you receive more input. This doesn’t mean that output practice is useless, however, because output practice can help you recall words you already know more fluidly, and cement those words in your memory. Regardless, my point is that you shouldn’t worry about output too much in the beginning, unless you happen to have friends or teachers to practice with: in that case, by all means, start using what you’ve learnt as soon as possible, and start finding out what works and what doesn’t. (Your practice partner will have to be willing to correct you, of course.)
Secondly,
I really don’t think it’s necessary to wait that long, even if that’s just… two months (?), which isn’t a huge amount of time in the grand scheme of things. I’m pretty sure WK’s recommendation is simply an attempt to reduce frustration among users, since even basic grammar resources have a tendency to use the most common kanji. However, honestly, provided you have a resource that provides furigana or rōmaji, you should do just fine even if you can’t read the kanji: when learning kanji, you should do your best to remember kanji, meaning and reading as a set with lots of links within it (here are some examples of how I’d approach it; you can start with the WK Level 1 list if everything else feels too advanced), but fundamentally, kanji are just visual aids that indicate nuance and help to distinguish homophones. As a Chinese speaker, I’m very thankful that they exist, because there are so many words that sound the same, but in theory, one could do without them given a deep knowledge of context. After all, it’s not as if illiterate fluent Chinese speakers didn’t exist a few decades ago, and they probably still exist now. Same thing with Japanese, I’m sure.
The real question once you start using non-WK resources will be this: what do you want to do about the kanji you encounter in such resources? Learn them yourself? Wait and hope that WK has them in its levels? It’s up to you, but I guess the first option is less natural when you don’t have much experience with learning kanji. I’d personally say do it anyway, and start by learning how to read a kanji aloud in context and how to write it, because that’s how I learnt everything, and I pick up new kanji quickly now precisely because I can guess how to write them and I simply store them as components in a certain spatial arrangement in my head, linked by how my hand moves to write the strokes, but other WK users are going to tell you that that will slow you down (I don’t think so, in the long run) and that it’s not necessary (that much is true). To each their own. All I’m saying is that my own methods have worked very well for me so far.
Finally,
Since you’re checking out courses, I’d like to recommend another one that covers about as much as Genki I and II while costing about half as much. I used the French paperback edition of this course, but they’ve finally released an electronic English edition, which is much cheaper than the print edition with the recordings. If you don’t have issues with working on a language via a computer, then I’d suggest you download the free trial (which includes the first seven of 98 lessons) and see if their teaching style works for you:
Assimil’s approach is essentially guided immersion: it offers a translation on one side, and a text in the target language on the other. Essential grammar and usage features are explained in footnotes. Kanji (starting from relatively simple ones) are used straightaway, and every lesson comes with an approximative pronunciation guide (except perhaps the final few). The advantage of this approach is that you get to see fairly natural Japanese immediately and you learn everything in context, which should make things more memorable and help you associate disparate pieces of knowledge. I also feel that it’s much faster than things like Genki, which include comprehension questions that are probably going to be useless for you on your own: you either know the answer and effectively end up copying from the passage, or you don’t know it and end up guessing, with no teacher to guide you. Neither approach is an efficient use of time as a self-learner, if you ask me. I prefer Assimil’s exercises, which require you to fill in the blanks with an appropriate word that you’ve recently learnt, or to attempt to translate a sentence from Japanese into English to check your understanding.
Some caveats, however:
- Some people feel that Assimil doesn’t provide enough grammatical explanation. I personally was only dissatisfied with the ways register changes and the continuous tense were explained. Everything else was decent.
- There were a few minor kanji errors in the French edition that I bought in 2015 or 2016. I don’t know if those have been fixed. There are only about five of them in total, however, so it’s nothing too serious, particularly given the value that the the course as a whole provides.
That’s my two pence. Hope it turns out being mildly helpful. All the best. 
I used Kanji Study at one point early early when I wanted to learn just by browsing, but it was a bit steep at the time. I learned stroke order more than anything, but now thanks to WK I am not so intimidated by the characters themselves, so I will check out their recall deck.