If I'm forced to lift in the AM I like to get up at least 90 min before it's time to lift. I take a hot shower for 15 min to get warm. Then I just move around and do stuff around the house for a while, drinking my preworkout drink.
Once at the gym, a normal warmup is usually sufficient (prehab stuff, a little band traction, hip mobility if it's a lower body day, foam rolling if needed). I might foam roll a little extra if I'm tighter than usual.
The hot shower is key though. I'm always cold when I wake up.
Try stretching your traps before training to avoid the tweaked neck. Put your right arm behind your back and grab your right elbow (or wrist) with the left hand and pull it across your back while trying to touch your left ear to your left shoulder. Hold for 30s or so and repeat on the other side.
That is by no means full-proof but it makes sense to me.