For sure such passes exist. The question is whether or not your company would pay for it. You would have to ask them.
Here's a web page that talks about shinkansen rail passes:
新幹線定期券の料金と学割|JR新幹線ネット
Rate from Tokyo to Shin-Yokohama is
東京〜新横浜 47,580円 (month) 135,610円(3 months).
So it's "only" about $450/month.
How much time are they giving you to find a place? Just a week or two?