According to the service manual, it is a Mikuni carb number BV21-17-35. It is Toro part number 55-2840, which as you say is no long available. I have been unable to find a parts breakdown of this carb on the Mikuni site, but will continue to look. My suggestion is to contact Mikuni and see if they have a rebuild kit available. Listed is a parts breakdown and service manual, which may help you. I'll let you know if I find some more info.
https://lookup3.toro.com/classes/doGetPub/?pubid=6931
https://lookup3.toro.com/classes/doGetPub/?pubid=2759