In general, the recipe is to eliminate all capture groups that operate on your large string. Beyond that, you can try to cut things off as you process them. Perl keeps a marker about where a string begins so if you're contientious, you can convince perl to just advance that pointer.

This is wasteful. When it matches, it makes a copy of $_ to an internal buffer so $1 can refer back to it. Eliminate the capturing parentheses and use substr() with @- and @+ to refer back to what $1 would have contained. The documentation for @- is a good reference for you right now.

You'll notice how I used 4-arg substr to directly replace the first part of the string.

            if (/\G<([^<>]*)>/gc) {
                flush_name();
                $state = 'TEXT';
                print OUT $1;
                next;
            }
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Efficient.

            if (/\G<[^<>]*>/gc) {
                flush_name();
                $state = 'TEXT';
                print OUT substr $_, $-[0] + 1, $+[0] - $-[0] - 1;
                substr $_, 0, $+[0], '';
                next;
            }
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