Lobbying for operators is best done at the appropriate perl6 language list(s). That's where the perl6 action is, and
that's where doubts like They may already be in development can be answered quickly.
The task seems to be too minor to warrant two new operators.
If you do this often, you ought to be using generalized functions like min and max, or even reduce.
I don't know whether perl6 will have here documents, but in perl5, =<< would be ambiguous.
=>> and =<< are not in the spirit of ||=. In the latter, the implied operator is first, the assignment later. With your suggested operators, this is reversed.
Perl6 will allow you to define your own operators.
Re: Thoughts on some new operators for perl (6 or 7)