The short story I'm looking for (which I think I read in an anthology about 10-20 years ago) involves roughly the following plot:
Humanity has found the means to travel between dimensions (or something analogous) but the only means to do this is to transmit one's consciousness to the next dimension where it is incarnated into a new body which is created there for it. The old body ceases legally to be that person and is destroyed.
An investigator is sent to a dimension a considerably distant from the home plane to investigate the status of research into the remains of an extinct civilisation which has been found there. For some reason this investigator takes the form of a tiger upon arrival.
His investigation reveals that one of the scientists was concerned that the activation of the machinery left by this ancient race could somehow cause a great disaster, perhaps the destruction of the entire multiverse, and wished to prevent this from happening. He was killed by the other scientist, but not before he could transmit a warning. This warning was received by susceptible minds throughout human history causing them to write stories rather like The Tempest, but couched in terms that they can understand (i.e. islands or planets rather than extra dimensions). Thus this, Forbidden Planet, and other fictional examples mentioned in the story are manifestations of the same idea transmitted back in time.
...this is probably a very rough recollection of some of the points but with luck it may prompt someone who recalls the name and author of the story.