No, I am sorry, I did not know, that JoomSEF does not work with Joomla since rel. 3.7.x!
I have posted my question also in a Joomla forum and they answered me, that Joomla would have a new rooting scheme from version 3.8 on. And it seems to me, that Joomla did change also something on the routing scheme since rel. 3.7.x
It seems best for me, to wait for Joomla 3.8 and then make new decisions concerning a SEF-URL component. But perhaps this component will not be necessary anymore, to get "speaking URLs" without ID numbers in it.
Til Joomla 3.8, my risk is, that ACE-SEF could become instable within the next Joomla Updates or it can have security issues. It seems, that I have no alternative solution than to pray and wait :-(