Reading this discussion, I'm starting to think that maybe some of the basic facts about Variola Minor that are being thrown around are either incorrect or have been misinterpreted. The reason is that, reading the information above it seems that it should have been much more likely for V. minor to have been the first strain of smallpox to cross the Atlantic rather than V. major. In that scenario, the fact that V. major was the strain to cross (was it??) seems like a freak accident of history that could easily have been avoided. These are the reasons why V. minor would have been the more probable candidate to cross the Atlantic.
(1) If it does spread faster than V. major, it should have been more common in the first place.
(2) The chance of a patient infected with V. major would survive a months-long sea voyage is likely fairly low as conditions at sea in the 15th/16th centuries were pretty dismal. Most adults would have already hadd smallpox as children, so the change of there being other people on the ship to pass the disease on to would have been fiarly low. On the other hand, V. minor, with its low death rate, could much more easily have kept its host alive accross the Atlantic.
(3) If the first carrier of smallpox to the New World was an African slave, and if V. minor is the version of the disease that was present in Africa (as one poster suggested) prior to eradication, it would seem even more likely that the first case introduced to the New World would have been V. minor.
Given that we know (do we??) that the version of the virus which more-than-decimated the Mesoamerican population was V. major, we are faced with either the situation that (a) this was a freak random event or (b) some of the information we are assuming about V. minor might be wrong. Here are some ways that (b) could occur:
(1) Maybe V. minor does not spread faster than V. major after all, or only spreads faster in populations with access to modern medicine. Maybe the lessening of symptoms also leads to a lessening of contagion, so that V. major would actually have spread faster in the 15th/16th centuries. Maybe since that time medical knowledge of disease vectors has increased so that in the 19th/20th centuries V. major cases would be easily idenitfied and isolated so that V. minor would actually spread faster.
(2) Maybe V. minor is actually a recent mutation that occurred after the 15th/16th centuries but before we gained the ability to distinguish between the two strains. This would explain why the strain that spreads faster (V. minor) didn't completely outcompete the slower spreading strain that kills its host (V. major). It was in the process of outcompeting V. major, but hadn't yet completed that process.
(3) Maybe the strain of smallpox that spread to Mesoamerica WAS V. minor and that, had it been V. major, it would have killed 99% of the population. This would mean that the "virgin soil" effect would be much greater than seems possible. I sincerely doubt this explanation but want to throw it out there.
Personally, I'm going with explanation (2) as there is a known tendency for diseases to evolve to have lower mortality rates over the centuries. This would mean that V. minor may not have been around at all at the time of the Conquistadors, and that the strain that infected Mesoamerica may have been an even more severe strain than V. major (which would explain the super-high mortality rates). But given the lack of any way of knowing which strains were around when, I'm totally willing to go with a TL that introduces V. minor to the New World before the Conquistadors.