Success!
The PowerEdge T30, it turns out, has three cables attached to the motherboard that the system monitors. The front panel intrusion switch can be disabled in the BIOS, so that eliminates the need for one of the three. The other two are a combo power button / LED cable and the USB / audio header jack.
I experimented with jumping pins on the USB header to see which ones detected the wiring harness, without much luck. These are non-standard plugs using 1.27mm IDC pitch connectors (a typical motherboard front panel header uses 2.54mm pitch). I did have a jumper that would fit those pins, but there must be more than two pins that detect the plug. Easy solution: I just removed the USB/audio jack from the Dell case and left it plugged in, tucked alongside the power supply. This left only the power button cable. These are a fairly standard part number used across multiple models, so thankfully the pinout is well documented. I spliced a couple of male 2.54mm jumpers with the power-button wires (in the link in the post above), then spliced the detect wires together using a 26 AWG button splice. At that point, I could plug the standard power switch header cable from the case into my Frankenstein'd connector.
Everything works as intended, and I've got a PowerEdge server in a RocketFish full tower case. This allowed me to bump the number of drive bays in the system from four to potentially 16. I've currently got 6 3.5" drives (8TB, 4TB, and a 4x6TB storage space for my Plex server) and the system is running on a 240GB SSD. The extra space allowed me to install a 4-in-3 SATA module, and I went ahead and pre-wired it with SATA connections and power. Next time I want to add drives, I've got four bays open and don't even have to dig the server out. The RocketFish case also has much better cooling than the Dell case; it has a 120mm fan intake directing air over the main hard drive bays, whereas the Dell case tucked two of the drives up under the DVD drive.
Admittedly, this is a lot of work when I could have just bought an off-the-shelf server motherboard, but I had a lot of the parts lying around, so I'm only about about $50 alltogether. If I ever do upgrade, the Dell can be returned to factory condition simply by re-installing everything and replacing the front panel cable.