Onyx and Caldera make it super easy to create your own profiles if you have an eyeone! If you invest the time, it will pay you back ten fold!
For me, the first step after I've created a good print profile/condition is to establish our rich black, which seems exactly what you are in right now.
It's important for us, as it sets our baseline for every print with rich black, until we need to create a new print condition. (most commonly due to new hardware)
Many times this is also when I prototype material to find the largest gamut, and best runability with my new hardware and ink.
I've done it now for 4 setups.
Once you have it set, you can consistently match any of your previous "blacks"
If you've setup your print condition properly it isn't too tough to print out a couple of builds that gradate, and pick the most neutral.
We started at rgb 0,0,0 in Illustrator and save as a spot color.
Working with an expanded or light ink set makes it a little more tedious
Document your steps so you can do this again...new hardware is inevitable!