First off, PS Audio has been one of the leaders in trying to implement a standard I2S protocol. Again, with configurable pin ability with even a single device, one should be able to find a setting to communicate with non configurable pin device.
As for HDMI vs I2S cable sound quality, I presume the HDMI should be equal to I2S assuming no signal being sent through unused runs of wire. The most salient point I see is if one is going for a high end cable, lets say all silver with expensive/complex labor intensive dialectic, shielding, there should be cost savings involved by having far less runs of wire.
As for usb vs I2S. I see almost no situation for which a quality implemented I2S shouldn't outperform usb. Galvanic isolation for usb in dacs is practically a given today. more at issue is the clock quality and power supply for those clocks on usb board, also with the needless complexity of sending signal through the usb board only to be converted to standard protocol of I2S within dacs. And then we have the issue of quality of I2S clock and power supply for that clock within dac. With quality I2S implementation via DDC we can take care of a variety of issues. First consider usb or perhaps other input feeding DDC, quality DDC optimizes and isolates that input, next, assuming we're going I2S we have the very real possibility DDC clock and power supply to that clock superior to dac. So, in my case Denafrips Gaia has paid great attention to the usb input (already have my usb optimized prior via Sonore OpticalRendu optimization and AQ Diamond usb cable), this in turn feeds highest quality OXCO clock with optimized power supply for that clock, this in turn feeds dacs via .1/2 M Tubulus Ximius (shortest possible cable preferred).
I don't care how optimized usb in dac is, I posit I2S should outperform based on no longer need to navigate detour through usb pathway within dac. Also, we have potential to use superior I2S clock and power supply for that clock in quality DDC vs internal clock and supply within dac. In consideration of I2S it is possible there may be some dac or dacs with highest quality I2S OXCO clocks and power supplies, in this case the DDC redundant. And I know there are some proprietary interfaces out there likely or proven to be superior to all the complexity of adding a DDC. With these exceptions in mind I'd suggest people try optimal implementation of I2S in any dac with i2s input.