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It sure looks like an encoder issue, especially the speed limit
(in one plot the encoder velocity dropped to 0 in basically an instant)

Did you set the encoder filter to 0 on all encoder channels?

I'm way out of my depth here but this may help:
www.gnu.org/software/gsl/doc/html/nls.ht...east-squares-example

Try this
forum.linuxcnc.org/9-installing-linuxcnc...-2-9?start=40#308037
And follow from there on.
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Getting permission denied from apt is strange, especially since you are correctly running as a normal user.
In about 90% of cases, if you get this error, one of the memory modules is on the way out, so it might be time to dust off your PC and check the memory.
If you do have another PC, you can install everything there and move the drive after finishing to this PC, that almost always works properly with Linux. Almost for me is 1 failed boot in about 500.

reading this might explain why it is returning a local minimum:
www.gnu.org/software/gsl/doc/html/multimin.html

 

So in my opinion we are using the wrong solver.