I did in the past print a very similar structure. A CNT for my work memorial cabinet. That experienced similar issues which I overcame with the usual anti-curling measures.
Note: Curling occurs when the newest layer is cooling down and hence shrinking. If that occurs on a curved path on top of a cooler layer, it will pull up the local geometry. The result is audible on subsequent paths. Where curling occurs again making it an amplifying defect.
- Adaptive layer lines: By lowering layer height on the overhangs, volumetric heat input was lowered so cooling was much more even. This drastically reduced curling.
- Slowing down: This is not really desired, but it is effective in combatting curling. Lowering acceleration is good too for the fine stems as printer needs a few mm to get up to speed, but only effective on short travel paths.
- Avoid crossing paths: Usually not a problem with PLA, crossing paths can become a problem where curling occurs. Use Monotonic for all surfaces and internal infill pattern and gyroid or honeycomb for Sparse infill. You probably do not have Sparse infill on that print, but curling is a generic problem.
- Double printing: In rare cases, there’s so little to print per layer that extending layer time may be neccessary. Since just slowing down to meet layer times only keeps the hot nozzle in the problem area longer, it can be beneficial to print two identical objects simultaneously or at least enforce a prime tower.
Hope this helps and 
PS: I did manage to print my final CNT completely without supports as the 30° angle was doable. Not sure about that end ring you have though.