You mentioned 復習, and I think that's the key. Try downloading
http://ankisrs.net/ and making cards for the words/kanji you want to learn. You can add audio and other media, and create cards with whatever model you want, even ones where you have to type in the answer. Using this method of study, you're able to structure the stuff you want to learn how you want to learn it. Let's just say you had to learn 2000 四字熟語 in three months: you could set yourself a goal of 22 cards per day and be confident that you'd get everything done by the deadline. It's worth reviewing the kanji you know this way as well, so you don't forget them. There are characters I've written about 10 times (including initial memorisation) Over the course of three years without ever forgetting them.
I'd also recommend upping your exposure. The news is a good source, but what about novels, manga, message boards, IMs with natives, Wikipedia etc? Try to find something that interests you, and it won't seem like studying at all.
As for 漢字検定, are you sure you want to start with 3級? It's tempting since you only need to know 1600 characters or so, but the real challenge is the massive amount of vocabulary you need to be able to write accurately and quickly. Apparently natives would need to study to pass Level Pre-2. Although, if you can find some past papers online and give yourself a mock test, you can gauge your level from that, I guess. I'm interested in taking it at some point myself, actually.
Anyway, this reply is slightly unstructured, but good luck with whatever you do.