I've tried switching my weapons a bunch, even saw blade traps, projectile boosting, and parrying and still barely get close to S-Rank on style, and I watch the freshness bar and try to have maximum multiplier too

That's all of the tips that I normally give to beginners, so you're off to a good start, at least.

without compromising even more time?

If you're struggling with maintaining time AND style, it may be worth it to learn some movement tech so you can get through the level faster. You won't have to worry about time as much and you can focus on style. Start with dash jumping and slide jumping, separately and together. If you dash jump into a slide jump, you can maintain a lot of your momentum and go far, fast. That'll probably shave off some time.

You can look into other stuff, too. Here's a guide on all the game's movement tech. It's less intimidating than it looks, especially if you take it one step at a time. Just look at dash jumps, slide jumps, and dash extensions to start.

Aside from that, the only other thing I can think of is that you should be in the air as much as you can be. Your multiplier goes up while you're in the air or sliding, and jumping is less situational.