The boards for the DIR9001 + PCM1793 aren't back yet, but the DIR9001 only going to 96 kHz only allows for half of the DAC's sample rate range to be used. Swapping the DIR9001 out for the CS8416 would fix that. They're backordered until the next ice age, but I have thrown together a design that puts the 8416 in hardware mode and configures it how I think it ought to work for the 1793.
Meanwhile, I have every confidence that the boards that arrive this week will work. I also have some confidence that I can put this on Tindie at $50 (board only) and in comparison to other products on Amazon that are using these same chips, I think the pricing may not be completely out of line.
EDIT: It bugged me a little that the oscillator frequency of the MAX1721 is about 125 kHz. For the 96 kHz variant, that doesn't bother me too much, but I really want the charge pump to run faster than the maximum sample rate for the board. I've discovered the SP6661, which runs at just under a megahertz, so that's going to be the device for the CS4816 variant.