qr/(?:$QUOTED|$NUM)(??{'' eq $& || '.' eq $& ? FAIL : SUCCEED})/
__END__
$VAR1 = [
          'name => ',
          '"foo"',
          ', fav.num => ',
          '3'
        ];
[download]

$VAR1 = [
          'name => ',
          '"foo"',
          ', fav',
          '',
          '.num => ',
          '3'
        ];
[download]

Update: Another way to fix the problem is to retain the test on $+ but make sure that the capture parens happen before the test (not around the test):

my $VALUE  = do {
    use re 'eval';
    qr/($QUOTED|$NUM)(??{'' eq $+  || '.' eq $+ ? FAIL : SUCCEED})/;
};
my $text = 'name => "foo", fav.num => 3';
my @text = split /$VALUE/ => $text;
__END__
$VAR1 = [
          'name => ',
          '"foo"',
          ', fav.num => ',
          '3'
        ];
[download]

Note that we still have to check for an empty match. Also note that in this version there are no parens around $VALUE in the split.

The empty match (that necessitates the extra check in the ...?...:... expression) is caused by something in $NUM, though I have not yet pinned it down. The following gives a glimpse of what the engine is up to:

my $VALUE  = do {
    use re 'eval';
    qr/$NUM(?{ print "($`)($&)($')\n" })(?!)/;
};

my $text = 'name => 5, fav.num => 3';
$text =~ /$VALUE/;
__END__
(name => )(5)(, fav.num => 3)
(name => )()(5, fav.num => 3)
(name => 5, fav)(.)(num => 3)
(name => 5, fav)()(.num => 3)
(name => 5, fav.num => )(3)()
(name => 5, fav.num => )()(3)
[download]

An empty match happens after each non-empty candidate fails.