Just changing Example 2 to this should give you the same result as with say:

$ perl -e 'use v5.10;for (1..10) {print "$_\n"; sleep(1);}'
1
2
3
4
5
6
7
8
9
10
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It is not even needed to deactivate buffering and change $|, since printing to STDOUT is line buffered (i.e. the buffer is flushed as soon as a newline character is found).