What is the best treatment to 'straighten' my teeth? Do you think Invisalign would work? (Photos)

I have previously had two retainer braces to fix my bite and push my top teeth forwards so that they sit in front of the bottom teeth. However, I feel the top teeth need straightening - the gaps between my teeth and my lateral incisors are slightly twisted. I have had an Invisalign consultation where she said it would work well. But, my private orthodontist said getting another brace would ruin my bite and my teeth are too small. Do you think Invisalign would work and sort my problems?

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