I had that happen to an engine. It had a lot of hours in it, and I always used dino oil. Changed to Mobil synthetic at one oil change, and the valve train became very loud and the noise wouldn't go away. It took 2 oil changes back to dino and 2 new filters, about 2 running hours apart, to get the valve train to stop clattering.
Most engines like synthetic, but some engines with a lot of miles or hours on them don't. As far as the filter check valves go, almost all oil filters today have a check valve. You can Google your specific filter and get the specs and be sure. The dealer will have no clue.
I'll bet you have a marginal lifter, and getting all the synthetic out of there will quiet it back up. Also, using snake oil additives to todays engine oils will not give you anything but a thinner wallet.