For starters, about the only combination harder to hit with on spanned hand might be ctrl-F5.
I've remapped my keyboard so that I push shift for numbers and leave it off for the various symbols on the top row. ^ isn't hard to type for me. (Plus, is it that hard to use two hands with shifted keys like you were taught in typing class?)
Can I assume that there is agreement already that in order to sit a beginner down and have them learn and write basic Perl, they shouldn't have to:
1) Remap their keyboard
2) Use characters that aren't on most keyboards
I have horrible visions of newbie Win32 coders getting frustrated when the only way they can see to do something is to open up the Windows Character Map program and copy/paste from there.
The current situation of the << and >> characters seems fine in this regard, because it's not something you are going to need to use until you get more advanced.
... ║ character as the default invocant method (to use that option as an example) is something I'd much like to avoid.