Sorry, I can't help with grammar books, but I have a few comments on what you said.
First of all, I advise that you should not avoid the Japanese characters, especially the kana. These play a huge role in helping you learn the language, as you advance with learning, romaji will only make it more confusing...
Secondly, Rocket Japanese has quite good grammar lessons, however these become useful only later on, as you advance through the course. As far as I adapted to this learning technique, I can say that it is easier at first to learn expressions and phrases just as Kenny gives them to you. Only after you get used to them, should you try understanding them and the way the sentences are structured. I'm saying this because when starting to study the structure of the Japanese language, you need to have somewhat a larger vocabulary, otherwise it would be very difficult.
Hope these hints will hell you with your learning, as it really depends on the individual how effective this learning style is :)