Writing is not a single task, as made plain by the fact that your plots and characters work but your style doesn't. In just the same way as a sportsman can work on a part of the game he plays so a writer can work on parts of the writing process that concentrate on strengthening weaker parts.
When I was younger the dialogue I wrote completely sucked, it just didn't sound like stuff people would say. I wrote a lot of scripts, specifically screenplays. It made things better. Screenplays also help with identifying the way to make something more show and less tell. For this reason I think that writing a screenplay could also be of use to you.
In a screenplay a writer has to be constantly asking if the scene gives a cast words to say and a director pictures to shoot. A great director can shoot loads of people talking a room and make it visually compelling but the writer can help by ensuring that pure exposition is eliminated wherever possible. Screenwriting mavens have a term for it: Turn your exposition into ammunition meaning take the things you have to explain to the audience and work out how to demonstrate that principle visually instead of just having a character explain it.
I never got caught in the exact situation you describe as I've only ever written fiction. One thing that revolutionised my writing style was when I chose to tell what I considered to be "a simple story". My key aim was to describe the protagonist journeying from point A to point B to do a thing, a quest story.
At the time I was trying to give myself an easy ride for the first time I ever attempted "National Novel Writing Month". The process of telling a story I figured I should be able to tell standing on my head opened up a whole number of opportunities for me to develop my general writing skills. For this reason you may want to write a story you feel should be well within your capabilities, your take on the saga of Beowulf for example.
The point is to do some work that forces you to concentrate on the weak point. The work should be simple enough to support you in your efforts and I imagine, although I have no actual proof even anecdotal beyond my own experiences, that going through that process will allow you to flex your skills at storytelling.