I found a solution. Scala reference says in section 6.12.3 Infix Operations:
The associativity of an operator is determined by the operator’s last character. Operators
ending in a colon ‘:’ are right-associative. All other operators are left-associative.
Therefore it was enough to rename >> to >>:.
It took me some time to realize that while a >> b is desugared into a.>>(b), a >>: b is desugared into b.>>:(a). So I had to define >>: as
def >>:(x: T): T = x >> this