Rule #2: Sometimes the power out will be much less than the power in.

Rule #1: In any power conversion scheme you will ever see besides all the ones you won't, the power out will always be less than the power in. You obviously don't appreciate the basic rules of power conversion, or you would not be trying to do this in the way you have chosen. I have only made a few simple circuits in my time, so I apologize if my terminology or references aren't that good. Someone suggested something like this but from what I can tell its not a voltage regulator, it seems like it just filters noise. I found this which seems to be a nice solution but only 10A and worried it may not allow the extra needed to pass for boot. I'm hoping for something I can place inline.

It would not boot using a 10A power supply, but it will boot on a battery since it can get the 12.5A it asks for to boot. The Mac mini when running in my tests idles around 1A but underload around 9A. In my search I have found Buck-Boosters but they seem to be not so clean and generate a lot of heat? I would think this is something fairly common to get battery voltage (10v-16v) and output it to a constant 12v? But in this case the amperage is fairly high (12.5A max but usually not more than 9A in my tests) I have it working but the computer seems to stutter and lag with the varying voltage of the battery instead of a constant 12v. I am in the process of converting a Mac mini to run directly on 12v and ditching the AC-DC power supply.

Test mac mini power supply