Crossovers that MUST be

[deadpan29]

I tend to take the view that a good story is allowed a cheat/handwave or two if that is necessary to set up the situation or otherwise get the story started.  Using methods of that sort to conclude the story is another matter.  If a consistent explanation can be found instead, that would be better, but IMO just saying the Garden make the transition to El Hazard with an earthquake as the only effect seen on Earth would be acceptable to get an idea with this much potential rolling.  Higher- or trans-dimensional effects might be more severe, justifying the TSAB reaction to these efforts.
----------
No, I don't believe the world has gone mad.  In order for it to go mad it would need to have been sane at some point.