If you're pretty much a "corkicelli," you don't need to relax to do an inverted bob. Here's a thread about curly bobs Curly Bobs Unite! What's to like about it.

I've worn my hair in a curly bob for the last four years. It's the first time in 30 years of wearing it curly that I feel that I have a style. I keep going shorter. As I tell my stylist, I want my earrings to show--but not my ears.

If you go really short, you may loose your curl is some of the 3a areas. As mentioned above, really short will be a problem to grow out.
3a (Corkicelli), highlighted, fine, low porosity

HGs: Anything Sevi; Curly Kinks Satin Roots, Curlycue ReNew and Coil Jam; homemade FSG and okra gel; soap bars; UFD Curly Magic; Botanical Spirits Jellies, CJ Repair Me, Aloe Fix