Is it possible that LED power supply is interfering with my webcams USB connection?
If you make the lights shine into a box, so the actual light doesn't make it into the room, does the camera still freeze? There might be an interaction/strobing between the LED light and the sensor of the camera, which might cause, or seem like, stuttering.

If the problem still happens when the LED bulbs shine into nothing, then it's a combination of the power supply and the PSU filtering in your computer. That seems unlikely to me, but I imagine anything could happen. Try another power supply for your computer in that case. Or try running the lights off a 12V car battery...

OR it could be EMI between the lighting wiring and the USB cable. USB is a high-speed protocol, and cheap USB wiring is not always up to filtering out external EMI. USB signal degradation can also cause frame drop-outs on webcams. Try a better cable (ideally with ferrite chokes on the ends) or if the cable is not removable, reposition the cable, or try another webcam.

Finally, the data sheet I found for that power supply by Googling said "life: 3-5 years," which doesn't fill me with confidence. I like equipment to last a lot longer than that...