tashippy, it depends on what you want to do. Do you feel like you need a big review? If so, then go through JFE quickly to review. Otherwise, I'd just move on to an intermediate textbook and keep challenging yourself. For myself, I definitely don't remember every chapter 100% in the book (I'm in chapter 10 right now), but I figure there will be enough repetition that I will keep moving forward even if I feel a bit rusty on some things.
vebaev, you would probably have a similar problem with Genki. Since both textbooks are for beginners and gradually increase kanji, there is going to be a lot of kana throughout the books. Towards the end there is less kana, but only 500 kanji are used total in JFE. Most beginner textbooks have this problem.
If you like JFE, I would just stick with it, ignore places it doesn't use kanji, and use an SRS (or whatever method you like) for vocab and grammar and put the kanji in your cards. Plus, the dialogue is supposed to be listened to, you aren't really supposed to read it anyway, right? :-)
In Anki, for example, I use the corePlus vocab deck and I go through and search for the vocab in each chapter in JFE and I put in chapter tags (JFE01, JFE02...JFE10...etc) This way I am getting exposed to the kanji for the vocab.
There is also a sentence grammar deck for JFE in this topic that you can use. I think it has kanji.
You could also try Bowring and Laurie's "An Introduction to Modern Japanese" which teaches more kanji, but both the textbook and required workbook are very expensive, and there is no answer key as far as I know.
Tae Kim's grammar guide has kanji in it too, and that is free.
Good luck!