The monitor profile does not factor in, and is not a factor because: a) I am not trying to make the print match the monitor, and b) no adjustments were made to the file before printing.
Actually, it very much does factor in. There are at least two things going on.
- When you're in Photoshop - unless you've chosen the monitor profile as your working RGB space - you're never looking at the chosen color space. Doesn't matter if it's set to sRGB, AdobeRGB, WideGamut RGB, or whatever. ColorSync is always converting the working RGB color to the monitor profile. It simply makes sense to do that since the monitor is the device you're looking at. It's the only color that counts since that's what you're basing all of your color adjustments on.
- When you print your image, ColorSync's entire goal (unless you're using a RIP) is to try and match the screen. So the working RGB color gets converted to the monitor profile, and then that gets translated to the printer profile's color space. That data is finally sent on to the printer.
And there's catch to all of that. What you're looking at is not necessarily the same as the the OS thinks you're looking at. All it knows is there's a monitor profile, and the working color is converted into that space. It doesn't automatically mean the monitor profile, in any way, represents what you're viewing.
Why is that? Because most people only use the canned profiles that come with the OS. Often, they choose an RGB profile that isn't even a monitor profile. But since the OS lets you choose it, it must be okay to do that, right?
No. Not even a little. The only existing profile you can choose that has anything at all to do with your monitor is the one pulled from the monitor, which is displayed above the line in the monitor settings. Such as here:

Why there are two in my list for the same monitor, I don't know. But I don't use them. Not even when a monitor is brand new. The supplied, default profiles are only good for a few months, at best. After that, the monitor will have drifted far enough away from the default that it's no longer useful.
Here's something most people also don't know. Apple plays with ColorSync's internal workings with every - single - major - OS - release. Every one. It doesn't matter if you haven't changed your monitor profile. It will no longer be used or translated by ColorSync the same as before. With every major release, I recreate my monitor profile, and all printer profiles.
The only good way around this mess is to use a true monitor profiling system so the resulting profile is based on actual readings of the monitor's output. Anything you do with the built-in Calibrate function is strictly a guess. And not even a good one.
X-Rite just came out with three updated monitor profiling devices.