You've had a few tangential suggestions, the ADB push being the fastest with the hardware and software you have currently.
I don't actually store files on my "PC" really as my source, I store them on a NAS and then pull them either to my PC or my other devices. This makes all my devices "stateless" as I find individual devices I'm moving around with ultimately break more often so I prefer the NAS route. My NAS is a Raspberry Pi running Rasbian with a 1TB USB hardd drive and a 64GB OTG flashdrive.
You can add to the other ideas:
- Airdroid which runs a small web server on your Android device and you access the Android device from browser on PC and push files, at Wifi speeds.
- run web server on your "PC" and then in Android just get them in a download app. My "PC" is Linux and its running Apache and I either SSH from the PC to the Android and then wget the file or use of the file download methods inside Android.
- USB OTG stick which also serves to augment capacity, I get about 22MB/s from USB to inside N10
One other indirect thing, is when you do a full Android flash wipe it seems to reformat and speed up the filesystem better than if you've done an upgrade, although I never benchmarked it to know, just an impression.
Nexus 5 stock 4.4.4 +ElementalX rooted, Nexus 7 2013 stock 4.4.4 +ElementalX rooed, Nexus 10 CM 11 rooted, OnePlusOne stock rooted.