IO::All comes to mind as a module which implemented overloading of "<" and whose technique might work for you. Didn't dig into that though, sorry for laziness.

update: couldnt resist... scratch that:

perl -MIO::All -E 'sub bo {"blorf"} sub ba {"bar"} ba < bo'
Unterminated <> operator at -e line 1.
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Nope.

To make that work - I fear (just guessing!) - you'll have to go all the way back to perly.c and modify that, fighting with the magic of "<>".

update2: this is bug smell to me.

update3: it looks like in the expression

foo < bar
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the foo thingy must resolve to something that doesn't consume what follows it on the right, overloading in effect or not, to be parsed as you want it to be parsed:

$ perl -E 'say < 2'
Unterminated <> operator at -e line 1.
$ perl -E 'say() < 2'

$ perl -E '(say) < 2'

$ perl -E 'say scalar(say) < 2'

1
$ perl -E 'sub foo(){1} say foo < 2'
1
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So, no. Using the LHS of < as a function which does or does not take arguments isn't possible, I guess.