Mixing manipulations on stereo signal will produce always the same scope of audible results. So if you play with mid/side and produce extremely wide side - it will not be more spatial, it does not work that way.
For spatial "binaural" sound you need different approaches, for example with hrtf reference database. Which wasn't done here (SM/FS) yet anyway.
The only good plugin I know, capable of producing relatively natual binaural sound (let me know if something is better) was made by Longcat, H3D. Actually they released app (for advanced sound tracking) and plugin (for basic manipulation), but the problem is - they no longer offer it. Just in case they stop activating the plugin, I created a virtual machine with it, so I can use it freely where I need.
When approaching binaural sound, there are few problems to keep in mind.
1) Back/forth switching. I use binaural setup for field recordings, in-ear microphones. They produce convincing 3D sound. But with no reference (visual cues, knowing the space), just headphones - everything sounds as if it was behind, although it was recorded in front. This probably could be compensated by additional mixing and filtering.
2) Vertical plane. Well recorded sound - can be perceivable in wide range of vertical axis, especially when the sound is close to the body; you can notice it down to your hips or even deeper.
3) Well recorded sound - sounds as if it was outside headphones, and not between them. Is "touching".
4) Person who records binaural sound - hears best spatial results; others may not perceive it that way. For example - while the person who records (with in-ear mics) and a group of similar individuals will perceive well the vertical axis (sound moving down to the bottom) - other people will hear it as if the sound was moving far away.
5) Listening perspective. If sound was recorded while standing up, and you listen to it while lying down - then sensory conflict may diminish the spatial effect.
6) Many hrtf based systems sound unnatural. It's the filtering curve. Even sounds recorded by inear mics - may need some re-filtering.
7) Slight head motion while live listening - provides additional cues. On offline recordings this probably can be compensated by a good model.
8) Binaural recordings are usually for headphones. But I know how to build a speaker system for that.
There are few other things to consider, but mentioned above are the most signifficant.
I was thinking on recording my own reference database for binaural plugin, but creating the plugin/framework is far above my skills. I think it would be good to have such framework here, in FS. Also there are few tricks to check on the capturing side, because from my measurements - there is something more than typical hrtf, and... I have some idea what could it be added in experimental design.