First reflections are not a negative as many speaker manufacturers take those first reflections into account when designing speakers and crossovers. Those are typically side wall reflections though. Floor reflections are usually avoided but if the hearth is only 20" deep, then again, the impact is not going to be that great. If the ceilings are already treated and the side walls have heavy curtains, the room likely has enough treatment already. A simple clap test can show if the room decay is too long.
The problem is that room acoustics are complex. A professional would take measurements throughout the room and address specific issues. Making guesswork and adding random panels is like throwing darts at the problem. It's hard to tell whether things got better or worse without measurements. There can be expectation bias that will lead one to think that there are improvements when in fact there was no real difference.
