Hi Andreas, sorry you havent had any replies yet. These threads can either take off or not at all.
I'm not too familiar with the Danish system.
I would suggest, when restrictions allow, trying to gain a UK (CAA) Class 1 as it is possible to gain one with an OML here (a friend of mine recieved his a few weeks ago with an SSL that turns to an OML when he works). Perhaps you can then convert it to a Danish Medical? Are you under the care of a specialist for these fainting episodes?
It may not be possible for you to gain even a restricted Class 1 with uncontrolled fainting with an unknown cause.
However, I'd be inclined to keep pushing to find the cause of the faining first-for your health's sake mainly.
The keys questions would possibly "What's your diet like, blood pressure and sugar levels, do you suffer from anxiety, or are you on any meds that could case these episodes."
To be given a Class 1 with an OML I believe the chance of incapacitation needs to be less than 1%, iirc.
Anyways, best of luck to you, explore all avenues and talk to every professional you can. What one doctor may not consider, another might.