I don't believe the particular video card you have has any form of audio device on-board, and so should not be interfering with audio in any way.
I notice the following in your kernel log files. Perhaps this correlates with when you lose sound?
hda-intel: IRQ timing workaround is activated for card #0. Suggest a bigger bdl_pos_adj.
I'd suggest seeking help in some Ubuntu-specific forum. or an ALSA support forum. Even though your description implies that the NVIDIA driver is causing this issue, I suspect the root-cause is something in the ALSA driver for your HW, or your audio HW itself.