You can run almost anything in the primary except vegetable oil, and even that might work. A high-tech synthetic isn't required in that environment, and those with moly or other friction modifiers should be avoided because of possible issues with the clutch disks. I use Castrol GTX 20w50, about $2.50/qt. at Wal-Mart, which works great.
I use HD Syn 3 in all three holes. Why should I not do this? When you say primary, I assume you mean primary chaincase, right? Not trying to be thick but my last bike was shaft driven and I want to be sure.
I use Bel-Ray Primary Chain Case Lube. Bel-Ray Big Twin Transmission Oil and Bel-Ray V-Twin Synthetic Motor Oil. Dealer recommended these be used.
A Harley Dealer??? I can't believe that! They usually just try to sell you Syn 3. You must have been talking to the tech huh? He's usually the only one with any sense...