hard to know without seeing the shape of your hair/face, you sound as if you have great foundations in terms of colouring and skin tone etc. When hair is really thick, I think the thing to avoid is a 'triangle' shaped hairstyle, i.e. with the widest points at the bottom.
Also, if you put a colour rinse (another similar brown tone, for example) through your hair, the added pigment can make hair softer and more manageable, and you can get that benefit without changing the basic colour.
Have you tried the Babyliss Big hair styler - it's very good for smoothing without going poker straight?