I do occasional smaller "takeouts" and haven't had any issues.
I have an "automatic album" (or whatever they call it) where all the photos of friends and family (even pets) get automatically added to it. Then I can just request a "takeout" for that one album, since those are the photos I actually care about. It's a much smaller download than the entirety of my Photos account.
I know you said you decided against it, but perhaps reconsider USB?
I was facing the same dilemma a few months ago, and ultimately decided that trying to break out those internal connections wasn't worth it. The problem with these tiny PCS is that they are not designed with arrays of drives in mind. There's typically not enough room in the case to properly add an additional drive, so you end up running the sata cord through a hole in the case and using an external drive and power supply anyway.
USB on the other hand, is intended to connect to an external device. The connectors themselves are more robust and they can even supply power.
I use my external drive for data I don't have to access constantly, like templates and backups. 90% of the time it's just sitting in standby. If you need to access a lot of data constantly, you might start to notice the slower USB speeds; if you can segment your data, keeping your "working" files on the internal drive and just use the external for storage, you probably won't notice the USB at all. It's certainly not the perfect solution, but with your particular restrictions, it might be the better tool for the job.
The other option would be Network Attached Storage, essentially a low power computer that just exists to allow other computers to access its storage. You can probably find an old, cheap desktop PC for sale locally, likely for less than it would cost you to bring out those internal ports and buy a drive enclosure and power supply.