From the pictures, looks like the damage to the fork is just chipping paint, not structurlaly compromized carbon. One option for peace of mind, you could strip the paint from your existing carbon fork and reinforce any suspect areas with an additional wrap of carbon fibre + epoxy to strenghten and then re-paint.
The stem/handlebar height in the picture is setup fairly high. If this is your preferred height, I would stay with a threaded fork + headset. Using a threadless fork at such high bar height requires a tall stack of unsightly spacers and/or a rising stem, just doesnt look nice on a high end racing bike. This bike would also look much better if you ditch the threadless stem adapter and get a proper quill stem meant for a threaded fork, this would also be a good opportunity to change the stem length if it does not fit you perfectly as-is.