So finally screen and eGPU pro made it to my desk, and as a many year apple user I was expecting a more or less: Connect and Ready to go experience. I got totally wrong here, it took me several hours on the Apple support which in this case proofed to be complete waste of time. As they blamed it first on the eGPU and then on the Display, then on cables etc. So I stoped that approach and went to Philips, while they couldn't help me directly (telling me however problem is known), they at least pointed me to a tool called SwitchResX which can solve the issue. Once installed I was able to just switch to the screen resolution and off we go...
So now I can use the eGPU to power the Philips 499P9H as well as the 65" SmartBoard I have in my office while reducing the load on my 2016 model 13 Inch Macbook Pro which makes it actually quite fast again due to the CPU constraint of the small GPU. I can easily use both screens with good speed, which was nearly impossible without an eGPU. As I will travel next week there is not enough time to clean up all the cabling, that has to wait until I get back, but so far I am actually quite happy with the new setup. No I just need my Moom settings adjust to the new screen estate and I am happy again aligning windows...
And in relation to the Smartboard it still looks small. But just to put it in comparison in front of the screen is my iPad and the table is 1.80m in width...