Thanks for posting your MDAT. Firstly, it is standard to take separate measurements of the left and right speaker, then both together. This limits what we are able to see. Having said that, I see quite a few problems.
First, why does it sound harsh and bright? Answer: because you have a lot of early and loud reflections.
View attachment 420038
This is your energy-time curve. According to Haas, all reflections arriving within the first 20ms are integrated with the main sound, which will both smear it in time and change its tone. To avoid this, the target is to have all reflections at least -15dB to the main sound, preferably -20dB. I have marked the main impulse with the green arrow and the reflections in red. You can use the timing of the reflections to calculate where the reflection is coming from. For example,
2 is 2.5ms delayed to the main impulse. According to
d = t/1000 * c (c = speed of sound, 343m/s), the reflection had to travel an extra 0.86m to the microphone.
1 is delayed by 0.66ms to the main sound. Because I have seen the step response, I know that it is the result of group delay from the woofer (a heck of a lot of group delay!).
View attachment 420042
Your RT60 shows the same problem. I took the room volume from your first post (I assumed ceiling height of 2.4m) and calculated the RT60 target in Acourate. I then drew in the graph over your measurement with MS paint. You can see that the reverb in your room is way too high.
View attachment 420043
Your frequency response is a bit off. Again, I took your measurement then drew a Harman target on top of it with MS Paint. Ideally, everything above the blue line should be trimmed to match the target, and everything below should be boosted to match the target. The blue line really helps you see where the problems are. That 60Hz bass peak is 10dB too loud. Worse, it is preceded by a dip, and followed by a dip, which will make it stick out even more than it should.
I don't know what speakers you are using, but there is severe lack of bass output below 50Hz. The shape of the FR curve makes me think lack of speaker output is the problem, rather than a room mode. The dip that you see at about 160Hz is definitely a room mode. It can be DSP'ed out if you are super anal about it, but you could just as well leave it alone.
View attachment 420044
And finally, here is the step response. We should not be looking at it since it is a measurement of two speakers together rather than just one, but let us assume for a moment that it is a single speaker. You can see that the tweeter and the woofer is not time aligned. As for the woofer, there are two peaks, which suggests a ported speaker or very early woofer reflection.
Recommendations:
1. Repeat measurement of left and right speaker individually. Ensure the measurement is taken properly - mic on a mic stand please. Do not use the mini-tripod that came with your UMIK-1.
2. The reverb is way too high. You need more furniture or maybe even room treatment to bring the RT60 down to target. DSP will not help you here.
3. Consider DSP to smoothen out the bass.