This is actually referenced in the article. You can use the Last-Modified date and the server will either return a 304 (Not Modified) or the modified image if it is newer.
pork has offered that you add a junk parameter to the end of a GET request and that should disrupt the cache, I'll need to read in to this. I'm interested in optimizing web speed as much as possible and this sort of thing and caching has always been something I've understood poorly.
Separately, the easiest way to get started with all these optimizations is to run the page speed check online:
https://developers.google.com/pagespeed/
and follow the recommendations, most important to least.
Turns out Google Analytics is actually doubling my page load time, but the data is too valuable to give up.
Anyway, thanks for the tips.