I'll have to think through this.
Like you , I used to create a custom profile for each still camera, starting with my 1DsII in 2004 I think. It really saved my butt on a fashion shoot, with orange/red/black checked slacks for a catalog. Hard to nail that orange! (red/yellow.)
OK. You can use a Color Checker with Color Passport or similar to create a DNG profile. You can also use something like i1 Pro to create an ICC profile, both basically via the same process - photograph some version of a Color Checker, etc.
The only software that I am really familiar with right now is CS6. I don't think it is possible to directly apply a profile in CS6 Production Premium. I am tired right now, up late with the election., but I can't think of a way in PP.
But you can open a video clip in Photoshop CS6. And any edits that you make there will be added as a "layer."
When you import that clip into CS6 Production Premium, you have the option of importing everything, or importing only the "Layers."
So if you go into Photoshop and apply or do a "convert to" a profile, you should be able to import just the Layer into Production Premium.
Then if you save that Layer as a standard tool, you could just open the file and drag that layer onto a "Sequence" in CS6, and you should have your custom calibration applied.
I have 2 of my cameras profiles in Lightroom 4.0 with DNG profiles. I think I also have an ICC profile for one of the cameras that I can try to apply in Photoshop.
I'll try to do that tomorrow and report back. I'll also take a look at other color tools in Production Premium, After Effects, and Speed Grade to see if there is a way to directly apply the profiles there.
I haven't been here for a while, so I don't recall what software you are using?