MoveIt motion planning - How should I splice several planned motion trajectories?

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If you simply connect multiple independently planned trajectories and retime them, you are not guaranteed a smooth trajectory. In fact, the motion will likely still be jerky, unless you blend the trajectories. Blending is currently not implemented in MoveIt, but there is an open PR that includes some blending functionality internally. You may be able to use that and the existing retiming functions to blend trajectories together, and then use the IK/PlanningScene to check if they are safe. In fact, if you do, this would be a welcome PR.

To answer your question in two parts:

1) "How do I connect trajectories?"

You can connect trajectories by extracting them from the plan you made (plan.trajectory_) and concatenating them. A RobotTrajectory is simply a std::vector of JointTrajectoryPoints in C++. You can google how to connect vectors.

2) "How do I use time parameterization?":

The AddTimeParameterization you mention is a PlanningAdapter. You can see what it does here, in the source code. You will notice that it calls computeTimeStamps, the retiming function for the IPTP algorithm. There are a few more you can choose, and which are listed in this tutorial. The interface should be roughly the same for all of them: hand in a trajectory, receive a timed trajectory going through the same points.