The super J-pole is easy to build and not easy to tune and impedance-match in the same time. When I filally tuned it and put it inside a PVC pipe, the tuning and the matching were gone. You must tune this antenna with the pipe in mind. If you follow my diagram, you will avoid my problems.
The diagram and pictures are self-explanatory. After building the antenna, you must tune it using a generator, directional coupler (to measure reflected power) and a power-meter. This antenna, if not tuned, is a useless piece of wire. If you cannot find a way to tune the super J-pole, change the antenna design to something that doesn’t need fine-tuning, like the collinear.
I tuned it by slightly bending the short part of the wire towards or away from the long part. If your dimensions are correct, this will be enough. If not, you may want to change the length of the short wire in 1mm steps.

The phase-shifting line (the one perpendicular to the long part) may be bent to fit into a pipe.It’s not a problem.

Obviously, this antenna has a symmetrical matching line that has to be connected to an asymmetrical amplifier or filter. The transition is done by a coil of semi-rigid coaxial cable (see the photo at the bottom). In my experience, I didn’t find a difference in performance with or without this coil.