Wow! Thank you very much for the link and this detailed response. This has helped clear up a great deal for me, especially as it relates to why I'd consider a single 16 channel solution, versus multiple 2-channel.
I fit into the "big but" category. I just need good enough to go from room to room.
I have wondered if I could just put two sound cards into a computer, but suspect it will lead to headaches. I see from your linked thread that the Lynx AES16 might be useful.
Now you have me thinking about using multiple stereo DACs -- would you have thoughts on which ones?
If sync doesn't matter, you've got a lot of options both internal and external. Multiple sound cards in the same computer might actually be the cheapest overall solution, but there are tradeoffs.
For internal cards, Asus and Creative both make eight channel analog output cards. I didn't mention them above because they don't have the ability to sync up with other cards. I've personally used both an Asus DX and an Asus Essence ST/H6 combo. Both cards have eight channels of analog output, one is about $80 the other about $250.
I have personally run two of these cards in the same computer without incident, but your mileage may vary. I will caution you though that while internal cards are the cheapest solution by far, they are more prone to pickup EMI from inside the computer (ask me how I know), and tend to have slightly flakier drivers than external USB DACs (also ask me how I know). I still use my ST/H6 in my secondary playback computer, so I obviously like it well enough, but be prepared that some troubleshooting may be necessary. If you could find a DX locally (i.e. meaning that you could return it if it didn't work in your setup), it might be worth it to try getting one, as you could use two DX's to get 16 channels for $160, and the DX (when adequately isolated) actually has pretty good electrical specs.
Externally, if you want to use multiple USB DACs, you need a computer with enough usb ports (or a usb hub with a high enough bandwidth, a USB 3.0 compliant hub should probably work if your PC has USB 3.0 support). I've never tried, personally, to use more than four usb DACs at once, so I don't have any experience regarding whether 8 would work or present a problem, but I can think of no theoretical reason that it wouldn't work. There are lots and lots of 2-channel USB DACs out there, but it's been a few years since I was in the market. Here are a few options (hopefully others will suggest more)
1) You might want to check out this blog:
http://nwavguy.blogspot.com/2011/02/behringer-uca202-review.html . He stopped posting in 2012, but most of the DACs he reviewed are still on the market, and he provides very detailed measurements about DACs. The specific DAC review I linked is a $30 Behringer USB interface, but he measured all kinds of budget DACs. You should be able to find info on DACs with a wide range of prices and performances on his blog, and he has nice comparison charts of various DACs.
2) I have a Fiio E7K which I've been quite happy with over the past few years (I use it to travel with), and I think I paid about $70 for mine. It's an integrated DAC and headphone amplifier, but it can provide a line level signal, you just need to buy an $8 add on, the L7. Fiio also makes other DAC options as well, as I recall the e10, has a built in line level output and is a little cheaper than the e7 because it isn't portable (which doesn't matter in your setup). Here's a link to a review of the e10:
http://nwavguy.blogspot.com/2012/01/fiio-e10-dac.html3) After measuring so many DACs, the blog writer above, nwavguy, decided to try and make his own DAC, and designed a two channel USB DAC called the ODAC, which is currently my favorite 2-channel USB DAC. It has excellent electrical specs, but it's a little pricier (about $100)
http://www.jdslabs.com/products/39/odac-objectivedac/To be clear, the DACs I mentioned would not work with a Lynx AES based solution, because most of them only have a USB digital input. If you plan to go the Lynx AES route, you need to find DACs that have SPDIF or AES/EBU digital inputs.