I've done a lot of Googling and been to a mechanic, but no definitive answer on this one yet.
It's a 2003 GMC Savana that runs great, once it's started. It's stubborn to start though, when I turn the key to the on/run position, the dash gauges and warning lights freak out for 5-10 seconds before settling to normal levels. If I try to start it while the gauges are jittering, the engine cranks but does not start. If I wait until the gauges settle, it starts perfectly.
As well, the engine will occasionally just cut out while driving without warning. If I slip it into neutral, turn the key to off, and then restart, it starts immediately.
Battery and starter motor were replaced a few weeks ago, but that did not help.
Given that the dash gauges freak out and settle, I'm 99% sure this is electrical. Maybe a weak ground connection? Possibly a bad ignition switch, though I struggle to see how that would lead to initial gauge craziness that would settle.
For the curious, here is a video showing how awful it was at starting before I replaced the ignition switch (thanks dlu!).