So (per your PM) your tranny still isn't shifting at any RPM when you set the low range? You've got the right pin to ground, and I'm assuming it's grounded for LO mode because that would make the most design sense. Might be that the PCM demands to see the TCCM pass its power-on diagnostics, not go back to sleep, and stay communicating. If the TCCM is there, and fails the power on diagnostics as 2002 TCCMs are renowned to do, then the PCM lights up the Service 4WD lamp. If the TCCM fails to talk at all on the bus, the PCM might just assume it's in a 2WD vehicle, and from that point on, ignores the LO range signal and doesn't allow the tranny to shift as expected because the ground speed never matches what it thinks the gear ratio is.
You might be able to fool the system by getting the VSS to report back a falsely high driveshaft RPM, but that involves designing a PLL circuit. THis may be an intractable problem. I can't figure a workaround yet without leaving the TCCM in and letting it control the actuator and encoder motor as if it's still running the show. For all we know, the PCM is expecting the TCCM to report back front and rear driveshaft RPMs over the data bus. That would be a real deal-killer if you needed sensors on the driveshafts. Crappy GM designers.
A tune might be able to get rid of that restriction, or it might be hidden in a safety-related subroutine the tune software doesn't have access to.
It's stuck in 1st? What's that crawl ratio, about 500 to 1?
And the brake light switch is still on?