I'm just a non-expert enthusiast, but I've spent a decent amount of time picking up little scraps of knowledge off the floor that the experts leave for me. The most immediate issue in most rooms is bass. This becomes even more true with a smaller room. 12x12 as a square is particularly bad, but since your room doesn't look to be a perfect square, maybe it's not so bad after all.
Some would say that it's impossible to go overkill with bass trapping. You are in a pickle with nice paint and trim, with one corner being the entrance. See, the corners are the best place to trap bass in many cases, usually with the front two getting more focus.
However, certain experts like b pape have never wavered so far as I have seen in saying that the back wall is extremely important, perhaps the most important, place to treat when you are up against it. Given the very limited placements you have to begin with, you might consider just continuing with the back wall.
Now you want to be assured that you place them in the best places. Well, it was nice for me to see Savant say that it's a lot like anything we do: taste. Like salt and pepper, add to taste, and experiment with placements too. When you have traps built, try them in the back, then prop them on the sidewall, then other places, and hey, where do they seem to make the most positive effect?
I could not tell you what the thresholds are, but the need for treating any particular boundary boils down to the delta in SPL between the direct audio and reflected audio, as well as the delta with time/delay. Of course, the closer the reflection is in SPL or time, the more likely it needs to be treated.
I am curious, how much open space is there right behind the speakers, and how much distance is there between the backs of the mains to the boundary?