Here's a quick fix I worked up here on my machine
At the top of the code for the login page, I added:

if ($query->param('safe_mode') eq 'true') {
     $$VARS{nodelets_off} = 1;
} else {
     $$VARS{nodelets_off} = 0;
}
[download]

and I changed this:

        $query->checkbox("expires", "", "+10y", "save me a permanent c
+ookie, cowboy!").                
        $query->submit("submit", "submit")
[download]

to

        $query->checkbox("expires", "", "+10y", "save me a permanent c
+ookie, cowboy!")."<br>".     
                $query->checkbox("safe_mode", "", "true" ,"Nodelets Of
+f.")."<br>". 
                
        $query->submit("submit", "submit")
[download]

This works like a charm, without any side effects (at least none that I've seen so far). It's just a suggestion but, knowing my experience-level, there may be security or other related issues that I'm not aware of.

Update if you want to see this in action, go here and just click it on and off, no need for a username etc. Once you click submit, it will adjust the nodelets accordingly.