I work aerospace composites for a living so I can offer a couple of sugestions. Most of the failures with composites occure for two reasons. First, for maximum strength get away from filiment wound tubes and switch to a multiply layup of Triaxial carbonfiber rotating the bias 30deg per ply. Number of plys is governed by strength requirements. Additionally you need to do a vac bag layup to achieve the proper density and strength. Second, and of equal importance, is get away from the hobby grade epoxies and go for a good aerospace grade, heat resistant system. Huntsman Araldite® MY 0510 is a good example but there many others. Fibraplex makes a great family of BMI (bismaleimide) epoxies that offer some of the best thermal resistant properties I've used. Website here:
https://www.fibraplex.com/BMIResins.htm . Once the layup has cured a high temp post cure will allow the structure to handle max temperatute exposures.
One factor that is almost always overlooked is abrasion/erosion. Much of the composite breakdown experienced is due erosion at transonic and sonic velocities. A good Fluoroelastomer paint applied to the nosecone and leading edge of fins will take care of this. Total film thickness should be 11-14 mils.
As has been pointed out, your goal is a major step up. At this level the appraoch needs to be less hobby rocket and more spacecraft. FWIW