Don’t know if this is the same issue for sure, but downdraft Weber carbs on Ford v6’s used to suffer from similar problems. The main reason for this, is the carb base where it bolts through the spacer to the inlet manifold can deform when it gets hot. This causes the fuel mixture to lean out and it only resolves enough for it to start when the carb cools down. The way you check, is to take the carb off and put a straight edge across the metal base diagonally and parallel to the sides to see if it is distorted at all. If it is, sometimes you can fix it by gluing fine sandpaper to a pane of glass or heavy metal sheet and rubbing the base of the carb across it to make it flat again. if this doesn’t resolve the issue then unfortunately it’s a new carb that will be required.
Another issue to check for is that the plastic baseplates can crack almost imperceptively, which when the plastic heats, up admits air below the carb causing rough running when hot and this is due to the air leak causing the manifold pressure to change, this leans out the mixture and that’s why it runs rough. One more thing to look for is the brass fuel pipe inserts where they meet the cast alloy body of the carb being loose and can cause fuel leaks. And lastly, check the butterfly spindles for excessive play on the spindle bushes….
If you have access to a fuel mixture (CO) checker, you could put it into the exhaust when it starts to run rough to see if it is running excessively lean?
To be honest, they are not great carbs in my opinion, and a decently set up original Zenith works really well, although I do believe that the SU conversion works well but I don’t have any experience with it personally. Hope some of this info might be of use. Best of luck!

The SU is a great carb and that's not just my opinion, there's a reason they were very successful on sports/performance cars.
On the series, you get a more instant throttle response and application of power which is useful when you're off road and generally a better driving experience