Well, after a lot of thought, I ended up going the build-it-myself route. Since the NAS is primarily for business and backups, I felt that data integrity was something I didn't want to skimp on, so ECC and ZFS were a hard requirement. But the FreeNAS Mini's restriction to 4 drives still didn't sit well with me, either. After a bunch of research, I ended up with:

UNAS-NSC800 chassis. I'm super impressed with the quality of this case, and would happily recommend it to anyone else. There are not many options for small form-factor cases with >4 hot-swap drive bays. This case comes at a premium over the one other case I could find, but that case would require using a drive bay as space for a PCI-e card.

SuperMicro A1SAi-2750F motherboard. Low power SoC, Intel Atom Avoton. The FreeNAS Mini uses an ASROCK mobo with the same chipset, with 12 SATA ports. The Supermicro only has 6, but I've been reading reports that people have been having problems with the NICs on the ASROCK mobo.

Supermicro PWS-203-1H Power Supply 200W 80-plus Gold rated. This was a mistake. I was looking at 1U power supplies that had a maximum length to fit in the case, and that weren't overkill. This seemed like it was the best option, based on power requirements. But I didn't check all of the dimensions of the PS or the chassis -- I (foolishly) made the assumption that a 1U power supply has a standard form factor in terms of width and height. Well, this one is designed to fit into a SuperMicro chassis, and it does not mount in the above case -- it's much too small, being almost (but not quite) Flex ATX. And no-one makes a mounting bracket, either. But rather than admit defeat, send it back, and find a different one, I opted to make my own mounting bracket from some 20ga sheet aluminum I had in the garage. That took a good two weeks of measuring (bought some new digital calipers, so win-win, right?), CAD (in OnShape.com), and metal work, but I was still waiting for parts to arrive, so whatever. I learned new stuff, and had fun. I made some mistakes, too -- Perfect-me wants to re-make the bracket, but since the worst mistakes are hidden on the inside of the case, Practical-me wins out, and I've moved on.

LSI SAS 9211-8i PCI-e HBA The chassis comes wired with a SAS/SATA backplane pre-wired with SAS cables, and since the mobo only had 6 sata ports itself, I'll need something when the time comes to fill the case. Easier to get it now, than later. It would have been nice to have had an external port in addition to the two internal ports (to be even more comparable to the Synology DS1815+), but I figure that since I'm only populating 4 drive bays now, by the time I populate the other 4 drives (with even higher capacity drives), fill those, and need to expand a third time, I'm probably several years away, if not more.

4 x 4TB WD Red HDD I'm not sure how satisfied I am with these, yet -- I discovered after purchase that some Red models still have the head-parking issue that the WD Greens did, so now I have to do the legwork to make sure that they're set correctly. I'm sort of wishing I'd gone with Seagate, now.

2 x 8GB ECC DDR3-1600 RAM

All in, cost was roughly the same as the FreeNAS Mini (but with more expandability) and Synology DS1815+ (but with better hardware).

Overall, I'm happy.

Having IPMI has been very nice, but there's been a learning curve to it, as the documentation is... sparse. For example, to mount a virtual floppy (I needed to re-flash firmware on the LSI card), it says you can upload a file that's named as .img or .ima. It took a couple hours to discover that uploading the image as a .img doesn't work, it has to be a .ima file. Installing FreeNAS via mounting a virtual CD was a breeze.

On to stage 2 -- configuration.

Thank you all for your input. It was very helpful.