I have to echo what others have said , it depends. Most times I will also go to an Escher with 5 to 10 and see where I'm at after a good stropping. I recently drank the kool aid and acquired a Nakayama and have done exactly what you described Kees. Escher first followed by the Nakayama.

One friend who has a lot of experience recommends doing it the other way round with the j-nat first followed by the Escher. I've got to try that. Sometimes I go to a vintage barber hone .... is there any other kind ? A Swaty or an iteapeech are favorites if using one of those. If I get satisfactory results from any of the above I will probably leave well enough alone.

If not I will redo the honing from 1k on up and sometimes I do that one way or the other. I've not had the Nakayama Asagi for very long but so far I'm impressed with it.