You don't need to use mnemonics to study using Heisig. The ordering is the most important part. e.g. you first learn 口 (mouth) and then 言 (say, word), then in the next chapter it could teach 売 (sell), before finally putting them together to form 読 (read). Since you should already know both sides to 読 it is much easier to learn.
Likewise, Genki teaches 時 (time, hour) as soon as it introduces Kanji, as it is a common character. However, there's a lot going on in that Kanji, which makes it difficult for a beginner. Instead RTK teaches 日(day), 士(ground, soil), and 寸 (drop, measure). It will then cover 寺 (temple) before later introducing 時, since you already know every component it becomes easy!
After the first 200 cards I stopped bothering with the mnemonics as -- like yourself -- I found them to be a hindrance.
As Matt says, Anki is brilliant. So is koohii.com if you struggle with intalling Anki.