I stared at the schematics in the sticky post and I think I have an idea that might work. If it does work, it should be relatively easy to implement in the form of a small harness that goes in-line with the connectors to the headlights.
First, some theory of operation for how each lamp is currently powered with the switch in the "Auto" position:
Day time - Low beams on ~60%, (low beams are PWM for DRL). Parking lamps off.
Night time - Low beams on 100%. Parking lamps on.
The LED signature strips are tied internally to the amber parking lamp within the headlight. Based on the logic above, the parking lamp signal can be used to swap the DRL signal to the parking lamp using a standard automotive relay.
The low beam power from the truck is diverted to the parking lamp/LED signature in the headlight through the normally closed relay contact leaving the low beams off during the day.
At night, the parking lamp signal is activated along with the low beams and this triggers the relay to switch the low beam power to the actual low beams.
The diode prevents the PWM DRL signal from reaching the relay coil and backfeeding the BCM but allows the parking lamps/LED signatures to function day or night.
The optional capacitor shown is used to boost the PWM DRL signal back to full brightness. This would be the same type of capacitor they sell for the HID relay kits to keep them from buzzing. Without it, the LED signature strips would be reduced brightness. I'm not sure how reduced but they're already pretty dim during the day so it's probably a good idea to add the capacitor.
There's another thread with a mod for the parking/turn signal bulbs that basically involves breaking off the terminals that go to the parking lamp filament so only the LED signatures come on. Combine this with that for a full package.
The headlight harness connectors are available from Mouser electronics, I bought all I needed along with relays and diodes off Amazon but haven't had a chance to build a harness yet. Total parts cost for a pair of harnesses was around $20 but I'm hoping someone with a little more knowledge of the truck's electrical system can verify my logic before I blow up my BCM...