I don't think the print head is the cause of the problems. The contact springs are located in the print head carriage and are not part of the print head. Other causes of the problem could be problems with the ribbon cables that connects the print head carriage to the logic board in the printer. The logic board could also have failed, so I think a new print head will bring no improvement. A damaged logic board can even destroy a new print head, so I would not recommend trying a new print head in the printer.
Force the printer into a deliberate error.
As you are now at a dead-end, why not try putting the wrong colour cartridge in the magenta slot and see what error you get, if any ?
Now we are getting somewhere so it’s exactly the same message that you got for the failed magenta cartridge (printer cannot recognize cart')
That would explains why you keep getting the same error message each time, the logic board is not in proper communication with the print head carriage unit and it can’t therefore correctly identify the different cartridge chips !
I reckon @PeterBJ picked this up straight away and identified the problem area as the ribbon cable or the logic board, so getting a new print head would be futile and a waste of money sorry..