For anyone that's interested, I took the step of eliminating the USB interface and purchased a Sonore Signature Series Rendu (v1). My thought was any contribution to the sound from the computer (assuming JRiver was configured identically) would be subtracted. This version of the Signature Series only has BNC and I2S outputs, so I had to use a USB to RCA XCore D to D converter and added an RCA to BNC adapter for the connection to the DAC. Without the Rendu, this interface sounded very close to straight USB, so a good representation of the potential change was possible.
Naturally, the sound changed from the introduction of the Rendu. To my dismay the sound from the new laptop continued to sound worse than the old one. To be honest, I didn't really care for the sound with the Rendu with either computer, but there was a preference for the old one. It still sounded fuller and with more body. At this point, I'm leaning towards trying a third laptop (I have one I can borrow) for confirmation.
Maddening.