I want one of these with an LTE modem on it so that I can drop it in the rack (non-datacenter) and remote-in regardless of the WAN condition.

At least the TinyPilot firmware is Open Source https://github.com/tiny-pilot/tinypilot - i don't know Pi-KVM. And it's a normal RaspberryPi with a debian-based os. So you should be able to just attach an LTE modem via USB and configure it via SSH, right?

pikvm is open source as well: https://github.com/pikvm/pikvm

In fact, TinyPilot is based on ustreamer, that is developed by Maxim Devaem, the pikvm creator: https://github.com/pikvm/ustreamer