Line 4 is still a lot of fanning-about, but it doesn't even compile

"@{[__LINE__}]" is a syntax error because you've swapped the } and ] - "@{[__LINE__]}" works fine.

some convenient token such as $LINE (or $__LINE__ or whatever I can just embed in double-quotes)

Nope, at least not built in, sorry. __LINE__ is like a function call, as of Perl 5.16 you can even write it as __LINE__().

Personally, I'd suggest living with the "fanning-about" or writing a helper function to output debug info (e.g. using caller). (Update: TIMTOWTDI - AnomalousMonk's printf suggestion is nice too. Personally, if it was a case where I didn't feel like it's worth it to write a helper, I'd probably write print "Line ",__LINE__,"\n";)

But since this is Perl, of course there's also a way to hack it:

use warnings;
use strict;

{
    package LineNumber;
    sub TIESCALAR { bless {}, shift }
    sub FETCH { (caller)[2] }
}

tie my $LINE, 'LineNumber';
print "Line $LINE\n";
print "Line $LINE\n";
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