Hello everyone,
I have some news regarding my issue and I thought I would keep you posted if it can help people in the future.
Like I said in my post here and on the PiKVM Discord support channel today, I ordered another adapter for less than 1€ with shipping (at the time I placed my order) on AliExpress that is recommended by PiKVM in their documentation, in order to try another hardware solution, should I not manage to find a software solution.
I received it today and it turns out to work just fine on a monitor I found, in all scenarios, where the other, more expensive adapter (~17€) didn’t.
I still have to wait for my replacement PiKVM to arrive in order to fully confirm that the new adapter works for my needs (my goal is to not use a monitor at all), but I’m pretty confident that it will.
So I will abandon the software solution, keep the new adapter, return the other one, and close this topic.
Thanks to everyone that took the time to read my post, even if nobody could help in the end.
Scentle5S