My final verdict, after examining all my findings so far:
- the root cause of my (and apparantly just MY) problem is a fatal combination of two issues: Navigon relying on specific system IDs and my tablet unwilling to 'alter' its generic SN data.
- The S/N change app I tried reported 'success', but showed the old and wrong one ("123456789ABCDEF") after each restart anyway, a first suspicious hint
- the permission controller tool DonkeyGuard does install, but crashes whenever started without even showing a splash screen, apparently losing the battle against my Android 5.1; another suspicious hint that matches the first one.
- the XPrivacy tool allows to block these IDs (useless); when trying to alter and save the critical ones it will show the randomly generated fake numbers but will not store them. As soon as I peek into the 'Settings' after saving, IMEI and SN are shown as '0000' and 'DEFACE' again. So it most likely feeds the original IDs to Navigon each time it starts, causing the 'an error has occurred' reaction.
- even the installation of the free trial version of Navigon exposes the same issue, on day #2, after working fine on day #1 (so they seem to check the ID not right away)
That solidifies my assumption that all these tools basically fail for a similar reason; with different reactions.

Quintessentially this means that my rooted China tablet, despite running on stock API 22 (Lollipop_MR1), uses internal trickery to prevent any attempt of altering the system IDs, for whatever reason.
Maybe the flashing of a new image or other Android version could solve the problem? But I am not willing to take chances just for the installation of this f.cking navi app.

What appears to be really needed is a version of Navigon that either circumvents these ID checks at startup entirely. Or that creates a random S/N value at installation time, that will be used inside this app whenever it is started later. Only needed for folks with a generic SN '1234..DEF' AND a locked down system that does not allow for the faking of real numbers. A miniscule number of users would benefit, no modder will ever go that route - bummer..

So Navigon DID win this battle against me after all - I lost the war.
Yet they did not squeeze a dime out of me either; so I will leave the arena 'heads up' anyways!
I wonder if they would refund me in such a case, if I had purched this frigging application that cannot work due to stupid verification checks?!


Most likely the modded version offered here in this thread is OK for most other users, just not me.
Sorry for the intrusion.