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That looks like maybe an electrical/wiring issue with the encoder.

Is differential signaling used?
 

Got some videos (or forum thread) of your setup? It sounds very interesting. Tube cutting subject is attracting:)

I'm posting screenshots from halscope. I think the encoder had some noise.

I am not sure why STARTUP_GCODE doesn't work - an example subroutine would help me investigate.
Usually for this sort of thing a preference file entry would be used. Any reason that you must use gcode variables?

is j3 the extruder or one of the rotary joints/axis?

I do have several machines with multiple configs, meaning one machine has several configs, made things very easy for tube cutters as i set them as normal 3 axis machine and use a config for each diameter tube.
That way, everything is 2D so Inkscape is used for CAM and perimeter is used as width.
In daily use, this saves huge amounts of time.

I have several multi ton machines controlled by Mesa boards, never had a single issue, ever, been many years in daily use, just have a look on this forum and that is not all of what i did using Mesa as i forget to take pictures/videos very often.
Example :
forum.linuxcnc.org/30-cnc-machines/31792...fit?start=140#321649

Yes, if i recall correctly, that is one sensor for the toolchanger that tells the motor when to stop spinning, it also uses 4 more sensors in gray scale mode for counting the tools.
As for PLC, i never use them, nor do i plan to.
I use exclusively Mesa for everything, and no, i am not affiliate nor do i have any relations to them, their boards just work, 24/7 for years on end without a single issue ever, and their support is the best on planet earth, as you can find out on this topic/thread, i needed non standard firmware for the existing absolute encoders and got it from them the next day, Try that with any other company....

See the downloads page on how to install the RTAI kernel and RTAI LinuxCNC version, they should be much better for latency on older hardware.
Also, always use --show for latency histogram, in your screenshot you can see excursions on both sides of the base period plot.