Citibank is your best bet and try the Otemachi branch. However......

My significant other got a bank account there without the normal requirements particularly without an alien registration card. However, she does have an official visa, but we are not in system and not registered with the ku, etc.

Normally, as a local resident you need to get an inkan (stamp) and then have this registered at the ku to get an official signature, which is essential for your bank account opening. The ku provides a certificate verifying your inkan that you bring to the bank. In lieu of this, a foreigner can go to their embassy and get a notarized signature document. (Although a foreigner with an ARC can of course get an inkan made. You obviously can't buy an off-the-shelf one at Lawson for 100 yen!) This is a PITA because the US embassy has up to 3 weeks wait (!) to get this and charge $50 for the pleasure. We only needed this to register a car. Luckily, Citibank did not require this to open a bank account.

The problem is that the Japanese are very inflexible if anything is outside the box, so my guess is that you won't be able to get it unless you have someone who will pull strings for you.