It's possible to put addresses corresponding to different streets on a single building by adding them as points inside of it. The best way (imo) is to map the entrances and set the house number / street of each entrance, I believe this is possible in StreetComplete (it's definitely possible in SCEE). As for the corner address, it will most likely correspond to one of the two streets...finding out which can be a pain, but in this case we may be able to figure that out based on adjacent house numbers & the interpolations that exist.
You're right that this is a nasty one though,  I can probably survey it later this week