I too studied kanji through Heisig. At first, I started only with learning the meanings, and then I got a bit greedy and added readings. There's nothing wrong with that, and if you can do both, by all means do them, but it was distracting to me, and it slowed me down. Suddenly my stories turned from being useful and funny stories that stick, into meaningless, paragraph-long stories stuffed with readings, various meanings, etc. It became like reading academic passages, and I couldn't bring myself to look at them. So I just went back to meanings and blazed through the kanji. It was faster to me that way than doing both together.
I didn't have experience with your issue as much as you do, because I mostly exposed myself to a lot of listening before I had ever started reading. That feeling of seeing a word, but only the English meaning pops out rather than the reading. I did, however, experience that with lesser known kanji and vocabulary. But that didn't last for long, primarily for two reasons:
1. Listening a lot
2. Audiobooks, anime/drama/movies with subtitles in TL, podcasts with transcripts, etc.
Concerning number 1, I listened A LOT. And I still do. Increasing my listening exposure likely increased my exposure to vocabulary, and more likely than not I had already come across the word I was listening too in question. Especially if it's a word as common as "homework," which you'll definitely find in a lot of school dramas and anime. As your vocabulary grows, the unknown words will start to stand out, and as a result, you will pick them up a lot faster through context, or by looking them up. If you listen a lot, you'll find yourself learning a lot of words without necessarily knowing what their kanji ever looks like in writing. Likely, you'll have known your kana, so you can input them in kana in an online dictionary, and among the various homophones that all sound the same but have different kanji, you'll be able to tell exactly which one it is because you already know it's meaning. Learning kanji meanings was truly a blessing to me. It made learning the readings bearable, and kanji overall is not painful at all. Sometimes, writing out the word when I see it, reminding myself of the stories and how the kanji connect, will be enough to burn it in my brain for a very long time. Then, with some more exposure, I never forget it. That's how it was, for the most part, with me. I still remember, for example, 手柄 (てがら), meaning achievement or accomplishment, after only seeing it once, I think in the subs of Fullmetal Alchemist, because I already knew the word previously through watching the series, as well as knowing the individual meanings of the kanji.
2. Audiobooks are amazing. There's
http://how-to-learn-any-language.com/forum/forum_posts.asp?TID=6241 this log on HTLAL, and even though most are classical books, the collection is extensive and you may find something you like. A lot of words I was able to pick up originally by sound, and then later looked up their kanji as I did in the example above, and it has been helpful. For example, the word 銀河 (ぎんが), meaning the Milky Way or the galaxy, from a story by Miyazawa Kenji. If not audiobooks, you can find podcasts with transcripts, news articles like FNN news, anime and drama with subtitles, drama cds (radio dramas), etc. Or, if an anime is popular enough and you can't find subtitles for it, read the manga if you can, you'll find the dialogue almost word-for-word.
I learned a lot through exposure to audio. Sometimes, if I've glazed over a word I heard somewhere but didn't know it's meaning, and then if I come across the same word as I read, if I know the meanings of the kanji, sometimes the sound of the word pops out and I think, "Oooh,
that's what this word meant!", or something to that effect. Try to accompany almost anything you read with audio of some kind. You can try Rhinospike for getting audio of text you have that doesn't have any, but I haven't actually tried it, so I don't know, and it can be a bit time consuming, in that you have to wait and all. I just use a lot of what already has audio. It's important to me because pronunciation is important to me, but listening teaches you a lot more than that.
You'll still come across words where you fill drilling makes them work. And that's fine too. The above is just making the process much easier for me, rather than drill the entire language.
That's what I basically do. I don't use SRS, so I can't comment on that (I tried subs2srs, but fell off the wagon a week ago). Early on, I tried RTK 2, but again burned out pretty quickly. I think it's useful, it's just me. But I do put words in a word document or a spreadsheet, and look at it regularly, just to make sure I don't forget the common words. But lots of reading for me acts like a natural SRS, so I'm trying to do a lot more of that, consistently.
In a nutshell, read and listen a lot, and match your audio with transcripts as much as you can. As your vocab improves, and your sense of how a word should sound like does too, you'll be able to infer more and more frequently what a kanji you've come across sounds like. At least that's what I've found through my own experience.
I found that because of the kanji, listening was so important, as I would have probably had to go through kanji books to do so, and I hate rote memorization. I'm good at it, but I just really hate it, and it slows me down because I keep putting it off.
You can also use Kanji in Context, or if you use Jpod101, the lists of common words with their audio and kanji are provided. I think using a premade list can be very useful, and may act as a short cut, I just never stick with one, except ones I have made myself and put in an excel sheet or something and periodically review. Whatever you do, listen a lot, and read a lot too. It's not easy in the beginning, because there's still so much to know, but you'll get there fairly soon if you stay consistent. Good luck! Let me know what your thoughts are.