I got the LED strips running off the computer power supply this evening. The power supply is on the top shelf in the center of the photo. I built a shelf in floor joists to hold the power supply, but didn't have quite the right wiring to make it a permanent installation tonight. The LED strip on the left is the brighter 5050 SMD LEDs, while the strip on the right is the dimmer 3528 SMD LEDs... Those are going to be replaced.
Shocking no one, the adhesive on the LED strip, which was shipped across the Pacific Ocean on a slow boat from China, did not hold up. I'll staple it in place soon, just like I did with the 3528 strip on the right (which will come down as soon as I get another 5050 strip).