How do I robustly tilt a strength-1 wall? Background

I am still working on my model of a ride-on mower, which has a seat that looks like this:



As you can see, the seat is mounted onto an inclined surface, which I realised to my satisfaction and which causes the seating area of the seat to be inclined as well. However, this means if I build the back of the seat in a rectangular manner, it will be inclined forwards, which is unrealistic (and uncomfortable for the driver). Therefore I need to tilt it backwards.

Goal

I have a 6×1 wall mounted onto one side of a regular 6×n plate and want to tilt it by at least 10° and at most 40°. With regular hinges, this looks like this:




However, if I use regular hinges, the result is not very robust and the wall falls down easily. I am therefore looking for a more robust solution.

Some specifications:


Whatever is needed to tilt the wall may not extend below the plate. (I need that place for something else, namely the complicated mounting.)
Whatever is needed to tilt the wall may extend somewhat forward (onto the plate) on the sides (resembling the above seat) but not backwards.
All components should be available in black. (I used red in the examples for better visibility.)
The inclination may begin somewhat above the plate.
My best solution so far are minifigure legs (which are pretty robust on their own) combined with a clip tile to hold the wall in place: