If I remember correctly I had a proco midi cable from sweetwater which was found to be 3 pin discrete wired, I think all HOSA midi cables are now 5 pin discrete wired, Im using the HOSA pro series which just means it has the removable ends vs. a molded end. The roland website says the gold midi stuff is 4 conductor so I believe it should be 5 pin discrete wired as the 4 conductor wires go to the left and right of center pins and the bare common wire is the center pin. Guitar center sells HOSA midi cables if you have one nearby, could be a quick and relatively cheap way to test and verify its not the cable... They usually have cable testers at the store and might be able to tell you directly if there is a problem with your cable. That is of course assuming they are open for business.
The dragon also has trs inputs for channel changes if I read the manual correctly. The switch dr has the 2 sw inputs as well. You could wire those up and try switching channels that way?