After a request, here is an alternative mix of Teo Torriatte using the same technique I applied to my other mixes. Unfortunately this isn't instrumental throughout but the choruses are (except the choir at the end) and only harmony vocals are audible in the bridge. To sum up this technique doesn't work well with any quiet parts of a song (vocals and just one instrument) only if the vocals are in one channel. You can still hear vocals in the verses but it's reduced meaning you can hear more piano.
But here it is for you enjoyment. Sorry it's an MP3 file but it's still enjoyable to listen to.
This is a very old technique that has been used for decades, even in analog equipment. With the restrictions you're applying it (no level adjusting, no hi or low-pass filtering, no phase cancellation other than 180º), it will only work with whatever was originally centered in the pan and it would be better when that is dry (effects tend to be stereo). Unfortunately that will mean that the result will be in mono.