I have not seen your ticket (or your message from DreamHost informing you about your disablement), so I’m just guessing here, but it seems to me they likely just set up an .htaccess file to forbid traffic until you can fix it.
“Logging in to WordPress” to disable plugins, or implement caching after the site has crippled a server is “too little, too late”; the time for those kind of fixes is before a server is hammered! Turning your site back on running WordPress during a crippling traffic spike will just subject other users on your server to more damage.
I cannot answer for the support staff who answered your ticket, and I don’t have full access to the details of your circumstances from my location here. What, precisely, did they say when they informed you of the disablement? If you still have FTP access, and the site is disabled via an .htaccess file, have you considered just renaming your domain’s web directory (that is holding the WordPress installation) to something else, and then creating a NEW directory for your domain and just placing a static HTML version of your page there till the traffic dies off? You could then re-enable your WordPress site and prepare properly for the next time (or make other arrangements like a PS server, etc.).
A “stumbleupon” wave of traffic should not cripple a static site … just saying!
You could probably get a cached copy of the page from Google cache, or your own browser’s cache, if you don’t already have one, and place that there so your “post” still gets read (and add a note to it explaining it is a “temporary” site/post to keep your server alive until you can get things fixed). That way your visitors could still see the content they came for, and you could “survive” the rush!
–DreamHost Tech Support