Have your realtor take you outside of the Yamanote loop. Oops... you said Ken Corp. I don't think they even acknowledge that anything exists outside of the Yamanote loop. In my area, there are two buildings side-by-side, built from identical plans. One is managed by Ken Corp (or at least it was when I was looking). One was, at the time, managed by Tokyu Community. For identical 93 m^3 apartments with mirror-image floorplans, Ken's price was 400,000/mo and Tokyu charged 230,000. If either of these places were located in Roppingi or Hiroo -- 600,000/mo easily (a Ken Corp person actually showed me one before I managed to convince her that I wasn't interested in living in the very center of Tokyo).

Unless you're allergic to public transportation or plan to party every night, there is no reason to rent a place inside the Yamanote loop -- let alone Roppongi, Hiroo, or Akasasa. You'll get more space for less money if you get out of town a ways. But you'll have a tough time getting Ken Corp to take you out that far. It cuts into their bottom line.

(BTW, the furthest I could get Ken to take me was Nakano. I'm still in Nakano, but definitely not in the Ken place. It's a nice neighborhood.)