Backtracking is something internal, and to mess with that, you ugly hacks. It would probably involve a new implementation of the regex engine to do what you want with backtracking.
To add the digits, you need to evaluate some code. With (??{}) it is almost impossible to evaluate and rematch, because when you try recursion, you can't easily use $1 over and over, because it'll be $2 (if you have a single set of parentheses) the second time. And you can't even use $1 within its own parentheses. Forget recursive regexes for now.
As I said, you need to evaluate some code, and you could try doing that with /e, and wrapping it in a loop. However, it's still nasty and there are better ways to do it.
Mathematics may be the answer to this problem. If you have a number, and add all digits and repeat until you have a single digits left, you're going through a lot of trouble to implement $digit = $number % 9  9 (figure out how that works yourself).
Illustation:
#!/usr/bin/perl w
use strict;
sub sum {
my $sum = 0;
$sum += $_ for @_;
return $sum;
}
for (1..10) {
my $copy = my $number = int rand 1e4;
print "=== Test: $_  Number: $number ===\n";
print "Brute force:\n";
while ($copy > 9) {
my @digits = split //, $copy;
$copy = sum(@digits);
print "\t", join(' + ', @digits), " = $copy\n";
}
print "Maths:\n";
print "\t$number % 9  9 = ", $number % 9  9, "\n\n";
}
=== Test: 1  Number: 5943 ===
Brute force:
5 + 9 + 4 + 3 = 21
2 + 1 = 3
Maths:
5943 % 9  9 = 3
=== Test: 2  Number: 3630 ===
Brute force:
3 + 6 + 3 + 0 = 12
1 + 2 = 3
Maths:
3630 % 9  9 = 3
=== Test: 3  Number: 3309 ===
Brute force:
3 + 3 + 0 + 9 = 15
1 + 5 = 6
Maths:
3309 % 9  9 = 6
=== Test: 4  Number: 8085 ===
Brute force:
8 + 0 + 8 + 5 = 21
2 + 1 = 3
Maths:
8085 % 9  9 = 3
=== Test: 5  Number: 117 ===
Brute force:
1 + 1 + 7 = 9
Maths:
117 % 9  9 = 9
=== Test: 6  Number: 8474 ===
Brute force:
8 + 4 + 7 + 4 = 23
2 + 3 = 5
Maths:
8474 % 9  9 = 5
=== Test: 7  Number: 8132 ===
Brute force:
8 + 1 + 3 + 2 = 14
1 + 4 = 5
Maths:
8132 % 9  9 = 5
=== Test: 8  Number: 1518 ===
Brute force:
1 + 5 + 1 + 8 = 15
1 + 5 = 6
Maths:
1518 % 9  9 = 6
=== Test: 9  Number: 6491 ===
Brute force:
6 + 4 + 9 + 1 = 20
2 + 0 = 2
Maths:
6491 % 9  9 = 2
=== Test: 10  Number: 2170 ===
Brute force:
2 + 1 + 7 + 0 = 10
1 + 0 = 1
Maths:
2170 % 9  9 = 1
There is a minor problem: 0 % 9  9 is of course 9, and you want 0. A simple && can fix it, I'll leave its placement to you.
I hope I've recognised the problem correctly. If this is not what you're trying to do (obfu? golf?), please forgive me :)
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