Room management - front or back wall dampening?

If they clearly understood your setup, I’d go with what they recommend. They are pretty experienced at what they do.

Has anyone followed some modest (modest as in not redoing the entire room) GIK advice for a small room? Did it make a noticeable/positive difference? What was the first difference you noticed?

Yes. Bass traps behind the speakers and panels behind my head (seating next to back wall). Made a huge difference took echo out of the room.

If one assumes they know what they are doing (and I’ve no doubt they do) you’ll get increased coherence, detailed/ articulate bass and a much improved midrange. Improvements no amount spent of hi-fi components could achieve.

I received some of their impression series panels. They are really nice! So, I just submitted another order yesterday for some of their alpha series panels. I needed some wall art anyway and these look better than most anything at a decor store. Highly recommended.
I may order more for non audio use around the house.

That is quite an aesthetic endorsement!