Also, no-one seems to have mentioned 'do'...

Yup, that's what I was thinking.

I've become increasingly fond of the do-block syntax; here's the OP's code with the two "do"s added where needed:

unless ($dontdothis) {
    dofistcritical() or do {
        dobackupcritical() or do {
            die "main and backup failed";
        };
        dobackupremainder();
        exit 0;
    };
    dofirstremainder();
    exit 0;
}
[download]