#Perl, 1116 1124 bytes, n=3, score=1124^(2/3) or approximately 108.1

Perl, 1116 1124 bytes, n=3, score=1124^(2/3) or approximately 108.1

Verification script

Not very pretty, but posting it because someone asked. I ran this several times with a variety of settings (typically changing $min and $max to check for various areas of interest); it wasn't a fully automated process. It has a tendency to stop running due to heavy CPU load elsewhere; when this happened, I just changed $min to the first value of $x that wasn't fully checked and continued running the script (thus ensuring that all the programs in the range got checked eventually). I only checked deletions from the first copy of the program, because it's fairly obvious that deletions from the other copies can't do more.

use 5.010;
use IPC::Run qw/run/;
undef $/;
my $program = <>;
my $min = 1;
my $max = (length $program) / 4 - 3;
for my $x ($min .. $max) {
    for my $y ($x .. $max) {
        for my $z ($y .. $max) {
            print "$x, $y, $z\n";
            my $p = $program;
            substr $p, $x, 1, "";
            substr $p, $y, 1, "";
            substr $p, $z, 1, "";
            alarm 4;
            run [$^X, '-M5.010'], '<', \$p, '>', \my $out, '2>', \my $err;
            if ($out ne $program) {
                print "Failed deleting at $x, $y, $z\n";
                print "Output: {{{\n$out}}}\n";
                exit;
            }
        }
    }
}
    
say "All OK!";

I've verified that this works with n=2 via brute force. Currently running a brute-forcer (with some optimizations to avoid obviously useless deletions) for the n=3 case, because with a program this complex, it's hard to check for radiation-resistance by hand; it's going to take a while, though, and I thought I'd start writing up this explanation while waiting for it to run. I've already verified that the outside wrapper (the section of the program with the most constraints on its operation) functions with any three characters deleted; thus if there is some combination of characters I haven't thought of that breaks it, it's probably going to be easily fixable.

Update: I've now verified that this works with n=3 via brute force (which took a couple of days); with a program this complex, it's hard to check for radiation-resistance by hand (and I made one mistake in a previous version, which is why the byte count increased). End update