So, listening to what GrandFather, Marshall, and others have said. Here's the refactored code:

use 5.010; 
use strict; 
use warnings; 
my ($fh, $str); 
open ($fh, '>>', \$str) or die "$!";
my $oldSTDOUT = select $fh;

$str .= qq[first line: \n];
say q[can we control the print from a sub? ];
sample( qw(1 2 3 ) );
$str .= sample( qw(4 5 6 ) );
say q[ well... ];

select $oldSTDOUT;
close $fh;

print_now( $str );

sub print_now {
    my $txt = shift;
    $txt =~ s/e/E/g;

    say "txt: $txt";
}

sub sample {
    print 'in sample(): ', @_, "\n";
}

__END__
## output 
txt: first linE:
can wE control thE print from a sub?
in samplE(): 123
in samplE(): 456
1 wEll...        ## the '1' from sample(456)
[download]

Lessons learned:

• open in append mode so we can add to the $str.
• anything going to STDOUT is redirected to the variable
• the legacy subroutine's print is appended to the $str when called inline, but
• the return value of the print is appended to the str when called in concatenation (scalar mode, terminology?)

Problem Solved!

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