So today, before I did the mod, I measured the voltage at the light bulb (by fishing very thin krynar wire to connector and pinching it between bulb and connector) with the engine running.
Battery: 14.42 volts.
low beam at the bulb: 12.48 volts.
high beam at the bulb: 12.73 volts.
I then installed the relay harness. Amazon.com: Putco 239008HW Premium Automotive Lighting Wiring H13-9008 100W Heavy Duty Harness and Relay: Automotive
After the install, I got these numbers:
Low Beam: 14.14
Here is a voltage vs lumens from Danial Stern:
10.5V : 510 lumens
11.0V : 597 lumens
11.5V : 695 lumens
12.0V : 803 lumens
12.5V : 923 lumens
12.8V : 1000 lumens ←Rated output voltage
13.0V : 1054 lumens
13.5V : 1198 lumens
14.0V : 1356 lumens ←Rated life voltage
14.5V : 1528 lumens Daniel Stern Lighting Consultancy and Supply