I wouldn't blame your host, actually. It's WordPress. It's a shame it's so often given a free pass on these issues when it really isn't good at handling peaks in traffic.
Using the popular caching plugins...W3 Total Cache (http://wordpress.org/plugins/w3-total-cache/) or Super Cache (http://wordpress.org/plugins/wp-super-cache/) seem to be well liked and I've used both of them without too many issues (I have some weirdness in my WP upgrade path). My blog has been on HN and reddit a few times and has never crashed, even though I'm on the cheapest Dreamhost hosting plan with what seems like 5 to 10 second response times for non-cached pages.
The only solution is to throw money at it until it gets better, isn't it? Or to wait it out. I remember when the word "Slashdot" became a verb, back when "Reddit" was a joke about a frog and a library book and DOS was what Windows ran on. The problem hasn't improved, as far as I know. So no biggie; it's not your fault. Ride it out and you'll be fine. Meanwhile, I'm mostly commenting so I can find your article again later and get to actually read it!
