Hi flo, HI Rob,
believe it or not, both the primary and the secondary IPA server are suddenly allowing web UI login again. This did not happen immediately after I requested the new cert as described above but somehow during the last few days.
The cert still looks the same, so I don't even have reason to assume it had something to do with that.
There was an automatic update to 4.6.8-5.el7.centos on Friday the 13th (hrhr seems to be my lucky day, atypically...) that also restarted the service. Maybe something in that update fixed it.
/var/log/ipaupgrade.log is huge.
It would still be good to know how such problems can be further debugged.