I've made the version of the board using the Si4734 the main version, at least for contest purposes. Besides the I2C interface, it has the benefit of using fewer passive components; that allows me to put in jumper wire holes so the output can be diverted to Analog input if need be (I have yet to investigate whether a couple of resistors would be needed for this, but rest assured I'll be looking into that).
One fun fact: the Si473x family has a pretty nice-sized data sheet, compared to most I've seen, though I've also seen worse. Speaking of which...
I've also downloaded a copy of the chip's honkin' big programming guide, though I haven't looked at it very intensely. One thing I have found is that the Si4734 normally has a fixed I2C address (0010001), but the SEN pin (currently left hanging) can be used to change it (to 1100011). Whether to hook that pin up to a select jumper (most likely a solder jumper) has yet to be determined.
I'm foregoing the chip's I2S outputs, at least for now. I'm not convinced that using it will have much benefit. I'm open to arguments to the contrary, though.
One bit that I'm not satisfied with is the number of via holes needed (6) to move connections between the top and bottom layers in order to get them where they need to go to. I'd like to reduce that, without too much twisting around of the traces; it's more important (in my opinion) to reduce the copper usage.
Meanwhile, I'm leaving the previous version of the board in place. If I go about pressing my own board, it's probable that I'll use that one, so I can escape the programming... though I may get into that programming after all. (Well, how hard can it be?)
EDIT: I only just noticed that the Feather's I2C pins "may need a 2.2K-10K pullup." With that, I've tentatively added a pair of 8K resistors for that purpose. Determining the actual proper value -- or even whether they actually need to be there at all -- will come later (possibly during breadboarding).