You have to strike a balance between fun and effective. I wouldn't recommend doing things that make you miserable, but also don't only use study methods that are "fun."

As for the titular question, if reading the cards is still a slog for you, try:

1. Making shorter cards. I do full sentence mining for my studying, so I'll sometimes end up with kind of long Anki cards. I think there are some purists out there who believe you should be able to go through your Anki cards super fast. I don't care, and I'm fine with a little more ponderous pace, since I go through my cards on the train, which gives me like an hour or so. However, if reading the cards is difficult and taking too much time, try making shorter cards. Short sentences, or even single-word cards. If the kana are still a struggle to read fluidly, probably stick with kana-only cards, and then move up to kanji with furigana, and then without the furigana.
2. I don't really practice my accent and somehow ended up with a passable accent. Luck of the draw, I guess. What I do practice is cadence: being able to speak at a natural and consistent rate. Anki cards are actually really good for this in my experience: you can just tap out the morae and whisper the words to yourself.
3. Try reading through longer texts you haven't read before. This will stretch the muscle of sight reading.

I would generally recommend reading the cards aloud (or at least under your breath). Japanese pronunciation is not very difficult, so any mistakes you have will probably just be in pitch-accent, and imo it's better to be able to pronounce words almost correctly than not be able to pronounce words at all.