I googled a bit and from what I've found I follow that it won't be easy to flush the Z2.log into the zope.out.
Writing the zope.out output into the Z2.log might be possible. We then would have to use Zope's logging system instead.
I'm sorry if this is disappointing.
If you want to know who did what at what time, my suggestion is to run the scheduling server with trace level 2.