Other than just cabling from my sound card into a couple of channels on the 24, is there another way to do this?
One additional way: In theory, you can save WAV files to an SD card, and import them as tracks directly into a Model 24 song without ever doing a D/A/D conversion. You would want to be sure to match bitrate and such.
However, the Model 24 does a straight import and has no ability to manage their location. If you do this after you have already started to record other tracks, they are very unlikely to line up correctly. You would probably want to add prerecorded drum / keys first, because you may have a heck of a time making it line up.
Is there better functionality with the 16 that would justify getting it instead and then expanding the inputs?
There is no substantial functional difference between the 24 and 16, other than # of outputs/inputs. (Still, there are some differences such as 100mm versus 60mm faders; graphic EQ; a few different controls; etc. You may or may not care. I got the 12 because I wanted the 12-specific features, in particular the DAW control. If I was choosing between the 16 and 24, I'd probably get the 24 because it seems worth the extra $200.)
However, there is a huge difference between the Model 12 and the model 24/16:
The 12 mixer is all-digital, while the 24/16 mixing sections are analog.
The 12 has the ability to act as a DAW controller; the 24/16 do not.
