Yeah, I can't stand soggy pickles either. And one of my brothers absolutely HATES beets XD. I love fermented beets, but I don't like them any other way. Carrot pickles are great, but you have to cut them into sticks, not shred them, because then they kind of compost and it's awful.
We usually eat our fermented cabbage with just about everything (savory) we'll have it with beans and rice, with meat. I've put it in sauces. I think I've even put it on sandwiches and wraps before. Sometimes we just eat it straight. When it's done right it's that good!
Putting black tea in your pickles will keep them crisp, but then they can taste a little like black tea, and that's not my cup of...well tea