my suggestion is to remove the shrink wrap and seal the ends with anchorseal or latex paint.  the ends will dry out fast and check.  even better would be to cut the log into blanks with the pith removed.  then if you can not get them on the lathe fast, seal the end grain.

I have used the shrink wrap to promote spalting with wet wood -- but the end grain needs to be wrapped or sealed.   The moisture will tend to move along the grain much faster than across the grain.   If you are seeking a good environment for mold growth you want the wet. 

Note that current research shows that specific molds cause the good lines and not as good moulds cause wood rot without the colors and lines. 

If you are not looking to spalt, cut out the pith so you do not get radial cracking and coat the ends to slow the drying/cracking.

Birch turns easily wet or dry.

Well, I stripped most of the punky wood and sealed the ends after cutting out three bowl blanks.
Had to kill a few bugs that emerged but the logs seem pretty solid.
The ends I cut off showed some impressive spalting.