Currently, I have Anki vocab cards that go English -> Japanese (Kanji) and Japanese (Kanji) -> English with both types giving the kana as a supplementary note. But I'm finding that I can't produce the kanji given just the kana. There's the obvious solution of making Kana -> Kanji cards, but that adds way too many reviews. I prioritize listening and reading comprehension equally, so is there a faster method out there? Could I get by with my original cards and listening practice?

http://jeffben.com/mcbs-part-1b-one-character-per-card/

This article might help. Though since you are trying to produce kanji from kana you can edit it in a backwards format like so:

(I'll use the same example sentence in the blog)

(Card 1 for 1st kanji production of the word 「学校」)

がっ校に通う
---------------
【学校】 a school


(Card 2 for 1st kanji production of the word 「学校」

学こうに通う
---------------
【学校】 a school

I made a few cards like this in the past when I was taking Japanese class in college for quick kanji quizzes. My 先生 would make her quizzes like ___校 and we would have to figure out the kanji from those context.
　(がっこう）

I hope this helps. I never used it outside of studying for class quizzes so I don't know how effective it will be for you.