$line = qq{10 PRINT "<29>This should be dim.<30>EThis should be reversed.<28>This is bold."};

my %fix = ( 
	"<29>" => '";@(-38);"',
	"<28>" => '";@(-40);"', 
	"<27>" => '";@(-35);"',
	"<30>" => "<30>",
);
    
$line =~ s/"([^"]*)"/my $s = $1;$s =~ s{(<\d+>)}{$fix{$1}}g;'"'.$s.'"'/ge;

#or
# $line =~ s/("[^"]*")/my $s = $1;$s =~ s{(<\d+>)}{$fix{$1}}g;$s/ge;