Is the internal drive solid state? If not it still might be worth it.

No, it's not solid state. There'd definitely still be some benefit if I upgraded it, but I don't want the cost of a large solid state drive; and while it sounds like a hybrid drive could help a bit with speed and still be cost effective, I don't know if it'd be enough of a boost to be worth it.

I've got a 2TB external drive on my XBox One, and that was a great addition. Really easy to do and meant I didn't have to swap games out, which is the problem I'm running into on the PS4.

In this scenario, you could update the primary HD to be a small (cheap) SSD for the OS only, then put a massive SSHD on the external port and see pretty significant performance gain.

Yeah, that'd be pretty sweet. I've got my PC set up that way and it's really nice :-)