f+3,1 is slow, but it may be Skarlet's only hit-confirmable launcher that hits crouching opponents. You can do f+3,1~d,f+3. If it is blocked, slide. If it hits, do the Up Slash and combo. On block after f+3,1, the slide is only interruptable by X-Rays and quick attacks with armor. I like 2,1,2 for punishing too, but some characters can crouch the first two hits, so I generally stay away from it.
I would train my opponent to block a lot of slides. You can then use the Red Dash, stop, and throw. You can even cross up. You can use f+4~d,f+3 too and slide which is only interruptable by X-Rays and quick attacks with armor. Aside from f+4,3, Skarlet lacks a great string. However, f+4,3 is only two hits, and in this game the motto is the more hits the better because of meter building and hit-confirming.