Confluence fails to start when hammered by "poll" requests

As seen on this support case, Confluence fails to start up when hammered by requests from
*/wiki/rest/mywork
*/wiki/rest/quickreload

even though these requests are supposed to be blocked by the DropIfNotSetupFilter.

From richatkins:

so, we're either not blocking them the right way for an upgrade, or we're doing something else bad when blocking them...