If your responsibility matrix doesn't change for every project, I'd just use the same over and over. Maybe make it a PDF or image to insert. I know, it isn't really the Revit way, and I hate hacks like that, but it would be better than creating more parameters and all the stuff. IMHO.
Alternatively, you could make a table in Word and include that in the spec book. That way you can use Word to edit for every project. I know, this isn't ideal either. Revit is really good with items actually in the model, but seemingly inflexible to create arbitrary things like tables. 2D detail also is an option, but a pain to format. I actually think if Revit ever lets us make a "pretend" table, it should be a 2D tool.
Just spit-balling here. None of the solutions will just be straight forward and simple.
I once created a table with abbreviations and abused a (by me) unused category. You could build something like that. it may look a bit different.
You also could see if you can simplify your table. Like have the entity supplying and installing the item be the same. We actually don't do any such tables since we leave it up to the GC to divy up the work. Like the plumbing contractor could run gas line, but so could the HVAC contractor. Or the controls contractor could runt heir wiring, but the EC also could run controls wiring. OR the HVAC contractor provides control valves, but that also could be by the controls contractor and so on. Controls contractor could provide the VFD, but so could the EC. Obviously, this depends on your specific bid environment and so on. I know you asked about the Revit procedure. But it doesn't hurt to think about the whole objective here. The more you simplify the table, the easier it is to implement in Revit.

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