Beyond "mid-side": decompose an audio stereo recording (coincident microphones) into Mid + 45° + 90°
There is a generic class of algorithms called &quot;upmixers&quot; that indeed de-compose a stereo signal into multiple direction and/or it's constituent directional channels. They typically work by chopping the signal into frames, evaluating correlation/phase/directional differences in multiple frequency bands, steering the origial signal on rules based on the analysis and then splicing them all together again.
It's tricky business and typically involves quite bit of trade off between the effectiveness of the spatial decomposition and spectral and temporal artifacts.
However, I'm not convinced that this would help in your case. You have a far field recording done in a reverberant space: the energy of your direct sound component (which is the only thing localizable) is probably tiny as compared to the energy of the early reflections and reverb. Trying to pull out directional components out of the reverberant field is hard and chances are they are decorrelated anyway, so applying time delays to them is unlikely to make much of a difference.
If you just want a little more space in the recording, you could try to boost the difference channel a bit with a high boost shelf filter. No boost for low frequencies, some for the highs. You can play around with the cutoff frequency, but I would vary the cutoff from 500Hz to 2kHz and do try boost of 2-3 dB or thereabouts.
If you are aiming for &quot;more natural over headphones&quot;, your best shot is to match the inter-channel correlation as a function of frequency to that of a human (or dummy) head in a diffuse field. At low frequencies the two ear signals are highly correlated, at high frequencies they tend be very uncorrelated and they are partially correlated in between. You can analyze the correlation of your recording and compare to a binaural target curve and then increase/decrease correlation at specific frequencies as needed. There are various ways of doing that, but the easiest way is to adjust the sum/difference balance: more sum = more correlation, more difference = less correlation.