Hello JAZ3, first of all I would like to let you know that I am using the same NUC with BIOS v0030 and I’m able to access the BIOS using an HDMI and a DP monitor.
If you did not have this behavior when using BIOS v0028, I would recommend you to please rollback the BIOS using the recovery method and check if the behavior persisted.
Also, you could remove all the components from the NUC (Msata, network adapter, memory) for about 20 minutes and restart the system again.
Are you able to access the operating system?
It could be also that Fast boot is enabled on BIOS.
I was able to access the BIOS with an older version (I think it was 0021) without an issue. I tried a couple of things to get it to prompt me about Fast Boot / skip Fast Boot, no luck.
I am able to run the OS (Windows 8.1) without an issue.
I'll probably either look for a workaround or the next BIOS update rather than rollback.
I’m going to send this as an FYI, but we were not able to replicate this behavior using the same device.