I don't believe you can do #3 and be code compliant. It appears what you're suggesting is to keep the existing 3 wire dryer cord and receptacle and run a separate ground wire from a connection point at the dryer to an appropriate point on the grounding system for the house. Code requires that ground wires be run in the same cable as the conductors. GFRE explained that there is an exception for the case where you are replacing a non-grounding receptacle with a grounding type receptacle. So, if you replace the 3 wire receptacle with a 4 wire receptacle, you would use that exception, ground the receptacle to an allowed point on the grounding system, and then change to a 4 wire cord. Unless you use that exception, a separate ground wire is not code compliant. I think I have that right, GFRE can weigh in.
Purely from a safety standpo "Its simple enough to make it better. Use a 4 wire plug or add a supplemental ground wire."
I said that would not be code compliant because the ground would not be in the same cable, assuming it is cable, which is reasonable. As GFRE pointed out, there is an exception that allows that. But to use that exception, you'd still have to change to a 4 wire receptacle and use a 4 wire plug. You can't keep the 3 wire cord/plug/receptacle and just add the ground wire directly to the dryer. That's my interpretation, again, GFRE can weigh in.