Just for anyone stumbling upon this.

TL;DR: If your Doogee V10 doesn't charge from USB AND wirelessly, it might be that a connector underneath the main circuit board came loose. The connector is located close to the battery, located directly underneath the connector for the battery cable.

I had my mobile phone stop charging suddenly, I guess when it "fell" quite a distance but seemed fine afterwards … truth be told, I flung it to show off.
It handled it fine in the past, so I didn't think of it and I didn't even notice anything was off, even a day later. Only when the battery started running low I noticed it didn't take up any charge … not from the USB port neither trough wireless charging.
I seldom used USB charging, to preserve the port, but all the info on the web concerning a Doogee V10 having charging issues was about the solder joints separating for the USB ports … that wouldn't break wireless (QI) charging, though.

I ordered a new charging board and battery anyway. After swapping out the charging board it worked, happily I put everything together and realized it didn't work again.
A few days later, I gave it another go, making sure to test after every step and I noticed that when tapping the main circuit board, where the CPU is located, the charging LED would go out or flicker. Looking closely, I noticed the connector underneath the circuit board stuck to the plastic frame and not properly seated.

What had happened is that the foam padding behind the connector, used to add some force and keep it seated, was completely mushed. This was due to the plastic surface not being smooth but just some fins. I added some foam tape to the area. Taking out and reinstalling the mainboard is quite a bit harder than the charging board. It's levered in there in a weird way, and the cable from the volume buttons just has a little clearance. Having a second pair of hands might help.

Anyway, after doing this, all was working fine, even with the metal plate screwed on and the screen taped to the case.
I didn't think of documenting the process, but I hope this text helps anyone out there. I must say the hardware looks quite nice in there and besides some smaller things, it's not just thought from the outside but has a lot of thought put into it on the inside as well. The software is definitely the weaker link.