If you reversed just one side, then one side was out of phase wit the other, with exactly the effect that you witnessed. It is important that polarity be the same for both channels for good sound and image.
Both channels reversed wouldn't be out of phase,merely left channel on right side and right on left,no? However for an adventure in soundstage I recommend Morton Subotnick "Sidewinder" it has deliberately out of phase synthesized bass parts mixed in with properly phased sounds.On elctrostats the sound seems to almost come from behind you.Definetly makes your skin crawl.
I'm guessing it wouldn't be any different than if you wired one speaker out of phase. The only problem I can imagine would be grounding. I don't really understand how turntables are grounded, but I do know that when the grounding isn't right, you can get a woofer-shredding hum through your speakers. Maybe someone who understands this can chime in, whether it's an issue or not?
If you exchange hot for ground for both L and R channels, you are reversing the phase by 180 degrees but the two channels will still be in phase with respect to each other. For those who can hear such a phase difference, it makes a difference in their listening pleasure. (One way seems more "right" than the other.) Problem is that no two LPs, and even sometimes no two tracks on a single LP, were recorded with consistent phase. So, if you want the luxury of optimizing for phase, I suggest you research phono preamps, some of the better ones of which have phase switches on their front panels or via remote. You might also do a search on these archives for more info on this subject.
What you did, reversing the phase of one channel, results in one channel being 180 degrees out of phase with the other. This gives exactly the phenomena you describe and is not desirable. One of the Stereophile test CDs demonstrates the effect when the two channels are out of phase with one another. I've heard it, and you described it pretty well. If you like the effect, by all means go for it.
Back when phono was my only source I deliberately connected one cartridge channel backwards, so that it was out of phase. Since most of the signal is common mode in the two channels (mono) this eases the load on the power supply of the power amp. When one channel pulls positive current the other is pulling negative. Of course one set of speaker wires needs to be reversed to get the audio back into phase. An added feature of this scheme is that a center speaker can be connected bridged across the stereo amp. A pot connected between the two channel signals at line level allows the volume of the center speaker to be reduced. Although this puts a low impedance load on the power amp, I never had any problem.
If you hook up your system this way, other source components, eg: tuner, need to be similarly phased, and it becomes a can of worms. For pure phono though, it works great.