saying that I would need to "work it into the grasshopper class". How exactly do I do that?
All I meant was that you would have to take the class I gave you, and cut it into pieces and put it back into the grasshopper script class.
You got most of it spliced in correctly, but I think we need to determine a couple of things about Rhino/Grasshopper before we can do much more.
You can get rid of most of the errors by removing the "Public Class port" and "end class" (the one before #End Region ) lines inside of the code you pasted. That's going to bring more errors though.
You will have to remove the calls to CPort_DataReceived and HandleComPort as they are used internally in the class and not meant to be called externally.
The real important question now is: can you call different routines inside the script class (from Grasshopper), or do you have to always call the run script subroutine? Once I know that, I can provide the last bits of guidance to try to get this running!