jrpnde asks:
is there any sort of experiments that can lead to a final room treatment that can optimize results before buying the rather expensive panels for that purpose?
Yes. What you want is Owens Corning 703
https://www.amazon.com/dp/B006FY7RHY/ref=dp_cerb_2 This is 2" but you can use 1", get one sheet of each if you want to test which you like best. Only slight difference as thicker absorbs a bit lower frequency.
OC703 is developed specifically for acoustic absorption and is used in a lot of expensive panels. It cuts easily with a razor blade, sheet rock knife or table saw. By itself, before covering, it is so light you can attach a whole panel to the wall with only some stick pins that make such tiny holes you’ll never notice, perfect for testing.
The most effective location to test first is to put 12" triangles in the upper ceiling/wall corners. Next is 8 to 12" wide by 3’ or longer strips vertically in the corners where the walls meet. Third place usually will be two pieces about 12" to 18" placed on the side walls at ear level to catch the first side reflection off each speaker.
Most people treat side walls with a lot of material to kill slap or flutter echo. The room is easily over damped, especially if it already has carpeting. This way uses a lot less material by treating only the most effective locations. Corners matter greatly because any sound emanating from a corner is reinforced by the walls. Damping in the corners is therefore much more effective than the same area of material on a side wall. Except the reflection points, where it has a bigger effect.
This is all stuff you can test and confirm in an afternoon and for cheap. Just like you asked.