To correct the overall phase rotation of the direct sound:
We need to see the phase rotation of the direct sound. With the mic at the LP the interaction of the direct sound with the room is very strong at the lower frequencies. Room modes and reflections cause the misleading data trace when the chart is formatted as was posted. REW has control settings though that will help us see the direct sound phase, that is, it will reduce the influence of the room.
> Remove all smoothing. [The posted chart shows 1/6 smoothing. If you select 'no smoothing' then the chart legend will show either a 'dash' or '1/48' smoothing. Either one is correct for this purpose.]
> Open the 'IR window' popup and add a 5 cycle frequency dependent window. Then select 'apply windows'.
This setting should remove most of the influence of the room reflections. The FDW setting may need to be adjusted though as rooms are different. We are basically looking to define the path of direct sound phase rotation amongst the remaining room influence. I have shown an example below. We just ignore the remaining room irregularities and look at the general trend of the trace as being representative of the direct sound phase.
[If the resulting phase does not fall smoothly to 0° at 20 kHz that means the Impulse is not located accurately at 0 ms. We can manually adjust its location as I did for this example. Note that, if any manual adjustments are made to the Impulse location it is necessary enter '0' into the 'Window Reference Time' and 'Apply Windows' to assure that the calculation of the phase is set to exactly 0 ms. Since in this case, you are looking only to correct <500 Hz a minor offset of the impulse near 0 ms will have no practical impact. It is more important for full range adjustments.]
If you have any trouble and want me to comment further, I would need the mdat file posted here.
I should note that others often suggest targeting the minimum phase rather than a linear phase, i.e., removing only the excess phase rotation. I do not really understand the reasoning behind that approach so I target linear phase.