Did you use a fine mesh bag for straining the fruit? Never made carrot myself, but IME the size of the mesh and the size of the pieces forming the pulp can make a difference. I also thought that with vegetable wines, you tended to boil the vegetable until soft. Did you let them get too soft?
The SG is good enough to bottle, so personally I'd bottle it and leave it. 1 year minimum I think for carrot.
IME the length of time the fruit/veg is in the bucket can also make a big difference. Apple I can go up to two weeks in the bucket for the intial ferment. Beyond that the fruit breaks down too much and makes the clearing process much longer.
I had a clearing problem with marrow wine a couple of years ago, because of the way the pulp broke down in the intial ferment, but knowing that has to be in the bottle 6 -9 months before drinking and experience with other wines, I wasn't too bothered.
Once bottled, whatever the wine, we put it under the house and leave it for a minimum 12 months. That gives it plenty of time to clear. If necessary just siphon before before serving.
Edit. We store our bottles vertically, so the fine sediment settling isn't a problem.