Since I had collected as much information from the broken AC adapter brick as possible, I decided to cut off the connector. This revealed only 2 wires which meant there is only one possible configuration. Both pins 1 and 2 must be 12V.
I grabbed one of my old computer power supplies, and fashioned a terminal connector to tie the 2 wires to the 12V rail and ground. I verified the 4 pins on the connector, plugged it in and my Helios4 booted up without any issues. I'm still waiting about a week and I'll swap out my 500W temporary PSU when it arrives.
For anyone with similar power issues, hopefully this thread may be helpful to them.
Here's the appropriate pinouts of the 4-pin AC adapter required for Helios 4 (see previous diagram for pin locations):
PIN 1: +12
PIN 2: +12
PIN 3: GND
PIN 4: GND