However, opposed to as is was before live updating to the current version I don't get the message that the "bglman.dll couldn't be loaded" anymore.
First, if you really had such error before ( and it would bglmanx.dll ), you would have very different problems than just Couatl not restarting in flight. If bglmanx.dll doesn't load, you wouldn't see anything, no Addon Manager menu, no GSX menu, and no Couatl menu, not even on the first start.
A Restart in flight, instead, only matters to Couatl, since bglmanx.dll, as a DLL, cannot "restart", since it only restarts together with the simulator.
I tried reinstalling, starting in various compatibility modes, starting as admin and without, disconnecting simconnect, etc. What else could I try? Do you know of any add-on that could be in conflict with couatl?
You shouldn't use any Compatibility modes, and you should never disconnect Simconnect, which I'm not entirely sure what does it mean, since Simconnect cannot be disconnected. It might be uninstalled, with a fairly complex procedure but, again, if Simconnect were missing/corrupted or had any other problem, NOTHING will even start
So no, your Restart in Flight problem must be something else which, as of today, you are the only one reporting it.
What other addons you have in the "Addons" menu ? You might try disabling all of them, by setting this line:
<Disabled>True</Disabled>
in your %APPDATA%\Microsoft\FSX\DLL.XML file and %APPDATA%\Microsoft\FSX\EXE.XML
Of course, you must left bglmanx.dll in DLL.XML and Couatl.exe in EXE.XML enabled, but turn off every other module. If the restart works with no other modules loaded, you can try to re-enable them ONE BY ONE, and try a new FSX session with one more module enabled, until you'll eventually find which one conflicts.