How to open gear box for Kenwood Chef XL KVL40?

Hi,

My Kenwood Chef XL is leaking oil from the gearbox.

According to this answer (Oil leak top of machine), the grease in the gear box might have dissolved to oil, and as the gear box seems to be unsealed, that oil is leaking. If that's the diagnose, then the way to fix it would be, to either replace the gear box (which sounds appealingly easy), or to open that gearbox, clean it, and put grease in again.

Unfortunately, the technically easier way of purchasing a new gearbox seems to not be simple; they seem to be hard to get, and also not cheap. So, what remains, is the pathway to open it up, clean, re-grease, and (omg) re-assemble in a way that it works.

Ignoring my fear of having to re-assemble those potentially millions of tiny cogwheels that might await me under the hood, I firstly wonder now, how to open the gearbox: I can see 6 phillips screws, but two of them are hidden under a big white plastic cogwheel. The gap between the cogwheel and the screw head is only about 5mm, so not much chance to get a screwdriver in between. I have carefully tried to pull it up, but it sits pretty tight, and I have little desire to break it.

Does anyone have a hint?