Precession, 2012 and confusing math

12.19.13.14.8 8 Lamat 1 Cen
I'm writing my NaNoWriMo novel, which involves (in no particular order), Deep Ones, a meteorite crashing into Earth, 2012, the Mayan/Aztec calendar, magical stones from outer space, Grand Cayman, Salem, New Haven, and a little more. (Hey, they say write about what you know)
I took a break to do some Mayan calendar calculations for a discussion two characters are having about the Long Count. (I'm SUCH a geek)
Now the 13th Baktun is supposed to signal a new world age.
Depending on who you ask (which culture) we've been through a varying amount of world ages, each one destroyed different (flood, fire, jaguars, etc). The 12-21-2012 end date points to another destruction of earth. (Which I don't believe, but for hte purpose of my novel I do.)
The beginning date of the first baktun is way back in 3114 BCE, in either September or August depending on which calendar you use, Gregorian or Julian. That's 5125 years ago.
Now the 2012 sun rising through the Milky Way and being reborn thing, as laid out in Maya Cosmogenesis by John Major Jenkins, postulates, as the earth wobbles (precession, a 26,000 year cycle) the sun will rise through the Milky Way 4 times, once on each Equinox and Solstice. This, being the Winter Solstice, marks a new beginning.
That's great. Except that 5125 times FOUR isn't 26,000. It's 20,500 5125 times FIVE is closer to 26000 (25625)--the actual precessional cycle, according to Wikipedia, is about 25,800 years.
So it's great that the 5125 fits so neatly into precession....however....it doesn't fit into the whole solstice/equinox thing. Either the ages are born every time the sun rises through the milky way on one of those four dates, making 4 ages per precessional cycle, or there are five ages per precessional cycle, which means the galactic alignment of 2012 means absolutely nothing.
This is troubling to me. I may go back and skim JMJ's book and see what he says; if he doesn't note the discrepancy I'm going to write to him. My friend John has his email address. (c)