AndreasF I am afraid you are in a medical black hole.
What did the cycle test show? I presume it was an exercise ECG and showed a drop in heart rate or blood pressure or you were faint. If your blood sugar was OK and you didnt have a dangerous heart rythmn your cardiologist may well have said it was loss of consciousness of unknown aetiology related to exercise. I agree with you it was 'caused' by exercise but 'medical cause' means the diagnosis.
Many young people faint and it wears off over the years. It is because of immaturity of the nerves to the heart, which may last into your 20s together with the ability of a young healthy heart to produce profound slow and fast heart rates.
I suspect many aspiring pilots simply fail to declare a faint feeling years before as they have been told 'it was nothing' and you have been caught by your own honesty.
It might be worth talking to the UK CAA especially if you do have an exercise ECG with a full report. They may wave it through on the basis of the above, they may allow you through after X years of no recurrence (and I do believe it will go away as you get older), or they may just say no as they dont want you blacked out in the cockpit having run up the stairs after a quick check A on a cold night.
Do not waste time or money on tests or quackery: ask the regulator. There have been posting about an initial class 1 with an OML in the UK