It might be a bit overkill, but you could run a caching proxy like squid on your client computer and redirect all your browsers (maybe all 1 of them) to use the local proxy. Then in the proxy you can more easily force caching of the content you want.
You'll have to use SSL-interception w/the proxy to see individual items, since google promotes SSL-obfuscation everywhere, you won't be able to see anything unless your proxy acts as a MITM.
Since I added SSL interception to my home proxy my caching rate has gone up to as high as 30-45% of requests, though more commonly its down around 10-15% of requests 5-10% of byte-volume.
I put in special filters to force image caching on some sites to improve performance. My housemate notices it when browsing youtube and how much faster browsing is now because the thumbs are cached locally.
It might very well be overkill for your use case, but it does give you a lot of access to things that are normally closed-off to users w/https-everywhere.