If it's stock then the pushrods are not adjustable so if you've owned it since new and haven't changed them it won't be that. As far as synthetic being noisier that has not been my experience in the bikes I've owned. My last bike was a wideglide that quieted down some when I switched brands of synth oil. My SG doesn't seem to care. My wife's sporty doesn't either. My guess is that the dealer will say it's normal as that seems to be the standard answer to any noise issue.
I have a friend with a Roadking that has an Evo motor. We put a cam, pushrods and lifters in it after he had a lifter go bad at about 50k. It has more top end noise than he would like and we've tried swapping, replacing, adjusting and everything else anybody could think of but it's still got a valve train noise. He's decided to live with it and so far there's no issues so who knows? In any case the dealer trip is a good starting point for you.