It appears that Qlik has a limitation in the MapObject:
"In Qlik Sense 1.X map has a restriction of 1000 input values only. Up to version 3.X map the value increased to 3333"
It does not explain the reason why dots were displayed better in some cases above, but looks like there is no easy way around it.
I've got some additional information from Qlik about possible workarounds, so will be investigating it further.