Sad to see that damage. I wouldn't use a quill post on these particular carbon tubes. I would instead drill holes through either side of the lug, use an aluminum seatpost, drill a hole or perhaps a slot in the post, and use a bolt passing through the lug and post, with a nut and washers, to compress the lug onto the post. I would use 1/4" thick aluminum washers and make them curved on one side, to match the curve of the lug. I would choose a post with thick walls, that fits the lug very securely (maybe even buy one that is a tiny bit oversize, and sand it down) and chamfer the holes. Then I would cut off the remains of the ears for a cleaner look.
This is probably the easiest and best fix. It's similar to how Hi-E Cosmopolitan frames mounted their seatposts.