what differences (if any) are there between the version of Shinto beliefs dominant in Japan when Commodore Perry arrived in 1852, and the version that would have been dominant in japan 750 years earlier in 1102?

According what I have been taught, Shinto is in essence a modern invention.

There was some form of native Japanese religious tradition before the introduction of Buddhism in the 6th century. And certainly some parts of that tradition survived in some form and are now a part of what is called Shinto. But we have no evidence by which to reconstruct what that original religious tradition was or meant. After the arrival of Buddhism and its victory in the Soga–Mononobe conflict those original traditions were completely subsumed into Buddhism. And all our written sources date till after this subsumption was essentially completed.

Why then do we speak of Shinto and Buddhism as separate religions? Now I was taught on ancient Japanese religion, not modern, so I'm not as knowledgeable on this process. But basically, as I've understood it: Starting in around the 15th century there's a growing nationalistic movement in Japan seeking a pure Japanese culture freed from foreign influences. This included wanting a pure Japanese religion to replace the 'foreign' Buddhism. What they turned to were those Japanese Buddhist traditions which had absorbed the most influence from the original native traditions (and I was taught very explicitly this is the most correct way to view it, even if at first it were native traditions absorbing Buddhist influences, at this point they were effectively Buddhist traditions that had absorbed native influences). These were then separated from Buddhism under the term Shinto (iirc the older term was Shindo (see here), which fell out of favour for being too Buddhist sounding).

These movement however weren't that dominant. As I said I'm a bit more sketchy on this period, so I'm not sure to what extent it did or did not gain support. But I do know that it only fully took off starting with the Meji period in the late 19th century. The new Meji government wanted to 'modernize' religion just like any other aspect of Japanese culture and society. In this process Shinto was reforged to emphasize Emperor worship and made the state religion. I believe there was also actual suppression of Buddhism, confiscation of land etc., but not sure so please don't quote me on that.

Now as this is all part of the nationalistic mythos, you will find some people being extremely offended at the suggestion modern Shinto isn't a pure Japanese tradition descendant from time immemorial. Just like you'll find some people extremely offended at the suggestion that the American Founding Fathers weren't all mainline Christians. But the above is what I was taught as the proper scientific and academic historical understanding of modern Shinto.

I haven't read it myself so I can't completely vouch for it, but I'd suggest A New History of Shinto if you want to delve into this deeper.