The way I calculate the Hebrew Calendar is not the same as the traditional method.

The way I calculate the Hebrew Calendar is not the same as the traditional method. To  my way of thinking the first day of the month is on what is called the Molad which is when the sun and moon are on the same longitude.  The basic issue really comes from the Gemara in Sanhedrin 10 and Rosh Hashanah around page 19 which seem to be  differing approaches (סוגיות חלוקות). I do not have a lot to say about this because the time I did this subject with my learning partner  I was not taking notes. I believe the chronological order was- we worked on the long Tosphot in Sanhedrin 10b very  thoroughly, and then the subject in Rosh Hashanah, and then we went to Bava Metzia.
[I apologize to the Jewish people for not taking notes at the time which would have been interesting as a very great learner was my learning partner.]  

Maybe a long essay here would be in order, but it would just be going through the basic subject with no new ideas.

Mainly, the idea is that there is no Sanhedrin to sanctify the new moon, and no record of Hillel the second doing so. So it makes sense to go with the Gemara in Sanhedrin that goes with the idea that when there is no beit din on earth to sanctify the new moon then from heaven it is sanctified. When is that? To the first opinion in Tosphot it is the Molad. But the other opinion that Tosphot defends is that it depends on when the new moon can be seen, which is hard to tell and there are no set rules for that.

The proof that the present day calendar was not in use during the time of the geonim is there are dates in their letters that are not according to the present day calendar. 

I admit, that if there would be authentic ordination סמיכה, then obviously we would go with the Sanhedrin. But there is no Sanhedrin, and you can not make up ordination that is not from Sinai out of thin air and pretend it is real. At that rate, why not just make up your own Rosh Hashanah also. If you want to ignore Torah Law, then, hey, go for it. But if it is Torah law we are interested in, then there is no Semicha and no authority to sanctify the new moon. So we have to go with R. Eleazar ben Azariah and the Gemara in Sanhedrin 10B.

I sadly have no Gemara to look up anything but from what I recall there is never a problem about the leap year because [if memory serves] all you need to Passover to occur in the Spring. [Certainly if you needed the beginning of Nisan to be in Spring, that would cause problems. But from what I know you only need either the 16th or 17th day of the month to be in Spring according to the Jerusalem Talmud. So Passover in fact always falls in the same month everyone else is doing it. The only difference is it will usually be one or two days before everyone else. ]