Interesting stuff. I have FiOS 40/40 service, and have none of the issues you describe.
I use the network 10.0.0.0 / 255.555.255.0 on my network (it’s faster to type. :) )
I *DEPEND* on the internal DNS of the FiOS router to run my network and DHCP services. Most of my devices are STATIC DHCP, and I have, at last count, about 25 devices on my network. The internal DNS works just fine.
I am using an Actionec MI-424 Rev D, with the latest firmware of course.