I don't think the time line is specified any further than the
Sengoku period which is
from 1467 to 1573... (but if anyone knows better please correct me!) Thus, the end of
Sengoku jidai overlaps with
Azuchi-Momoyama period, during which much of the unification took place.
I'd say run along with it.
It is fanfiction after all, if we can stuck them into alternate universes, why couldn't you tweak Takahashi intended time line a bit (if there IS anything more specified than
Sengoku period) to accommodate your plans!
Besides, wasn't there in the early anime episodes this guy with the clepto monkey? He was Nobunaga - though not Oda, like Kagome first assumed. So it's sorta already been done in canon, though as a gag. ;3