Just past 31 seconds is indicative of a power supply issue as well as the symptoms. That's ironic as you clearly took some precautions. Here are some thoughts:
Thick wires - good as this lowers inductance. If there's any appreciable wire length, twist them up. The twisted pair won't benefit you with this issue but will make your system less susceptible to nearby emitters as well as be less of a transmitter. This is a good general practice.
100uF bypass near power pins - good to have a nice size bulk cap nearby. You may need smaller caps as well for their higher frequency discharge capabilities. I doubt that is the issue.
The lab power supply is where I would point my suspicion. What is the voltage (presumably 3.3 as you're applying directly to device)? What is the peak current capability of the power supply? Does the supply have a current limiting feature and, if so, is it on?
The O2+ has a large peak in required current as the WiFi system comes up, right around 31 seconds. Likely something in your general power supply circuit is limiting charge to the device as peak charge is required.
Best of luck!