Why does ranging cause particularly large jumps

I’ve seen range jumps of 50+ meters due to this sort of effect so what you are getting isn’t unreasonable.
Your antennna is highly directional, any chance that some of the jumps as caused by the direct signal falling into a null while a reflection path isn’t and so you pick up the reflection?

Yes, you need to read the ACC_MEM, it contains pairs of I and Q values (around 1200). Calculate the magnitude of them ( sqrt(II+QQ) ) and then plot that.

It is normally reasonably symmetrical between the tag and the anchor, they will be close enough that if there is an issue it will show up in both.
I only use this as a debug tool when manually requested rather than for normal operation. Reading that much data over the SPI link takes a while, I’d rather throw the data out and use the time to make another range attempt rather than try to recover the range from potentially bad data.
There are some quirks on reading those registers, code to do it has been posted on this forum multiple times in the past if you hit issues.

As for how to correct the data, there are probably dozens of PhDs written on how best to do that. Personally I went with the throw the data out method. But then I’m using lots of anchors and a high update rate so dropping one or two anchors as they move through a bad zone isn’t a big issue.