Rationale :
Eh, I'm not so sure about being "too immersed". A few years ago some animated movie was shown at 40 fps instead of the typical 24, and I remember reading about how that made people in theaters sick as well. It's more likely people just get used to the framerate they play at, and after a while everything else looks weird.
Most people don't bother to cap their framerate at 30, if it gets that low it's because they're letting it run wild when they have a crappy video card. If a framerate is near 30 fps on its own, you can bet it's going to swing between 20-40 fps, which really is unbearable (imo). I think that explains why you don't ever really hear of people getting used to 30 fps, aside from last gen console gamers ofc.
It's also worth noting that I used to cap at 60 fps and it was fine. It's only after a year or two of a 30 fps cap that 60 fps looks weird.
I have used the adaptive Vsync (half refresh) option on my 120hz monitor, and again when set to 60hz. This allows for 30 FPS/hz v-sync, so it never varies, and this makes me nauseated very fast. It is extremely choppy, and the more the camera moves, the choppier it feels. This was not intentional, but the moment the game loaded at a locked 30 FPS, I could not tolerate it. I meant to set it to 60 FPS locked due to Skyrim's buggy nature at higher than 60 FPS, but I had previously done it through a lower refresh rate prior. The two stacked was unbearable.
That Japanese thing may have had some other things involved for that result, most people do not feel that way. If that 40 FPS animated show was shown on TV, then surely the problem was that TV's cannot display 40 FPS evenly due to their 50/60hz refresh rate. The Hobbit was said to seem weird, but I never heard any dizziness claims, but that was never displayed on TV at 48 FPS.
But other than you, no one has claimed that higher FPS gaming caused any downside. There are only 2 things that I've heard of and experienced that could possibly explain your problem:
1) Over immersion will allow for a real enough experience that motion sickness symptoms are possible. Otherwise known as simulator sickness.
2) Uneven frame rate, which should make a locked 60 FPS good for you. I don't know if you've ever tried this or not.
Edit due to your edit:
It's also worth noting that I used to cap at 60 fps and it was fine. It's only after a year or two of a 30 fps cap that 60 fps looks weird.
That would fit into my #2 possibility. It is not the low or high FPS that causes you problems, it is the uneven frame rate that causes you problems. With V-sync, anything other than a locked 30 or 60 FPS stutters mildly. Without V-sync, only partial frames are being displayed randomly up and down the screen, which looks like tearing. One or both is likely your problem.
Those are things I've heard people have difficulties with and why a lot of people shoot for 60 FPS with V-sync. Few can tolerate 30 FPS unless using a controller.
Possible better solutions for you:
58 FPS cap is unnecessarily low, you can use 59 FPS for certain, and possibly 60 FPS if your refresh rate never dips lower than 60. This sounds like it may still be an issue, but this is only an issue with CF/SLI in DirectX, or in the few DirectX games that use 3+ buffers by default (SLI/CF forces this).
A 85+hz monitor can give you the chance to use the high refresh rate, and cap your FPS at exactly half the refresh rate. You can make custom refresh rates with Nvidia and probably AMD, so you could try higher FPS rates that are smoother.
60 FPS with V-sync should have the exact latency as 30FPS capped with V-sync. Perhaps you could explain that further.
Of course G-sync with a 120 FPS cap would be the ultimate. The cap a few FPS lower than your refresh rate will be needed for the same reasons as Vsync with FPS at your refresh rate, only you don't have to worry about having it be half the refresh rate for it to be smooth.