i agree with susu.
the perm will do much more harm than good.
i say transition over time and snip a little away at a time or transition for a set period of time then cut.
if you feel comfy with short hair then you might want to BC now.
also, stop getting it colored. no re-touching the roots or anything.
the routine you have now with the air drying and dc is very good. so keep that up.
you can transition using rollersets, twistouts, braidouts, etc.
basically anything style that will match your naturally curly hair.
i dont know if your hair is dry, but if it is make sure to keep it moisturized.
especially the demarcation line, which is where the relaxed and natural hair meet.
hope this helps and good luck.