First: I don't think you're doing anything wrong. If you have the option of a whole room over a small chamber, obviously you go with the room. Also, SPCR is great (I'm a long time reader, despite my low number of posts) and I love the attention to detail in the writing here. I haven't purchased a case or power supply in half a decade without coming here first. You're definitely doing things the right way, in my opinion.
I'd like to play devil's advocate for a bit on this chamber vs room discussion. Since you're looking for an additional test environment, this might be relevant in SPCR's current situation.
The simplest way to explain this: As you get closer to a wall or intersection between two walls, the lower frequency sounds get boosted. This boost can start as high as ~300Hz, and its effect can be several decibels.
Let's say you get a 3 dB boost at 300 Hz. How would that affect your measurements?
If you're using A-weighting, the weight at 300 Hz is -7 dB. So let's say we're measuring a very peculiar sound that is made up of tones that drive both the 315 Hz and 1 kHz 1/3-octave bands to 100 dB. Unweighted, our SLM would read 103 dB (100 + 100), but A-weighted it would read 100.8 dBA (100 + 93). Add in the +3 dB change at 300 Hz and our SLM reads 101.5 dBA (100 + 96).
So that's a pretty extreme situation (the most extreme, I think), and it gives us an error of only 0.7 dBA, within Type I accuracy. For a real measurement all bands would have energy, including all of those non-weighted and positively-weighted bands between 1 kHz and 10 kHz, further diminishing the effect the 315 Hz band has on the total value. The resulting change in dBA would almost certainly be less than the differences between individual measurements of identical conditions.
Then consider that the primary noise source being measured is a small fan, which will have broadband noise with most of its energy 500 Hz and above. If the noise you're measuring starts out -5 or -10 dB at 300 Hz (with respect to 1 kHz), and then you weight it a further -7 dB, a boost of 3 dB in that band isn't going to have any noticeable effect on your A-weighted numbers. Even a 6 dB bump wouldn't be detectable.
So that's something to consider.
Another thing to consider is that it would be much easier to keep environmental noise out of a chamber than out of a room, especially at low frequencies. A box within a box is much easier to build at scales of a few meters, and large wavelength sound waves would be less efficient at permeating a smaller object.
Food for thought.