If the target site is already down(all or almost all requests got an error), you can switch to new still working target.
Something similar has been done on https://www.ban-dera.com/
Instead of “to ensure targets are "evenly" distributed.” (I.e. use full targets list) send them to e.g. first 20 sites ( order is important) and when some sites will be down, add more rows to attack.