I have been able to almost remove the jitter.  I have added a prism to refract the light. Using the prism, I can position my diode closer to the focal point and ensure it is hit in the middle.
I also realigned the first lens. I used a UV light, bluepoint2, with Norland61 and UVacryl2295 for final fixing. The prism is 7.5x7.8x8 mm. It was still in stock. The single spot is 25x25 micron.
A spot created by four facets is 48x60 micron. The cross-scan error is 23 micron. The jitter is 35 micron. The facet error was set to 1/3200. In general, the lower the better.
I still need to measure the lane-to-lane stability if this is done, I will proceed with experiments.
In the image below a pixel is 4.8 micron. Note that the spot become less sharp at the edges, as predicted by my earlier theoretical calculations.

The new setup with prism and photodiode.