Well I can confirm that they flex.
The only thing (un do able?) is to tie in the middle of the frame rails (chassis legs) to the front of the sills and/or tunnel. Currently the frame rails are only connected to the sills by just a 0.8 mm sheet flat floor under your pedals, and with a sheet of just 0.8mm of firewall to the tunnel.
The ends of the frame rails are connected to the sills via the floor and the seat structures. But halfway up the length of the frame rails, say at firewall height, it seems to be floating to me... This is where the small triangles may help, stiffening up the firewall.
I've seen quite a few cars with stress cracks and creases from continued flexing around the gear shift opening. On the left and right, running down in the direction of the footwell.
I myself put in a 3d contoured, 2mm u- shaped piece to reinforce the round opening, going 20 cm up front, and 15 cm to the rear, and plug welded it in. There are some pics in my build thread.
Strangely, i fail to understand for sure where the load is coming from: that area is not loaded directly, although the gearbox mount is not far off. I can only see it from torsional forces; pushing one wheel in the air will twist the car; this point (gear shift opening) is the cross point of the 2-axis over which the twisting occurs.
In modern cars, often there is also a vertical connection from the firewall/dash to the floor following (roughly ) the sides of the console. This adds a lot of rigidity. What type of vertical connection can we hide behind those center console panels....?