when you say v6.3 I assume you meant NBAM/NBAA 6.3SP1 on PRPC 6.3 SP1(DSM edition). Please correct me if i assumed incorrect.
I had a look at the upgrade guide of PM 7.13, I think you cant upgrade directly from NBAM 6.3SP1 to this. The upgrade says, if upgrading from older versions, you have to upgrade first to NBAM 7.12. and I couldnt find an upgrade guide for NBAM 7.12 but i suspect it expects upgrade from NBAM 7.11.
wrt to installing previous PM version on Pega 7.3.1 as part of intermediate upgrade steps, i am not sure if this is a good idea. I would prefer that both PRPC and PM versions be upgraded with compatible levels. Atleast till Pega 7.1.9. the platform difference is too big from 6.3Sp1 to 7.3.1, and you have to run the upgrade activity(RunPostInstall) to upgrade the Marketing artifacts, i am not sure how this activity will behave for ex running upgrade 7.12 or 7.11 upgrade activity on Pega 7.3.1.
so my suggestion is to upgrade both Pega and NBAM/PM in steps.
i didnt understand your question, which upgrade guide you are referring to?
We have 2 products here, one Pega Platform and other PM, some PM versions are compatible across multiple Pega Platform (with additional hotfixes). for ex PM 7.22 is compatible on Pega 7.2.2 and Pega 7.3, but not on Pega 7.3.1.