How old is your chain?...these are generally the symptoms that indicate your chain and sprockets are not long for this world. ...and yes, you do want to replace it before it possibly replaces your engine cases or you.
Iin the OP, he did say all was new as of this Spring.
Personally, I am no fan of non-Oring chains. I'm assuming the bike is the CB750 in your signature? A very good non-Oring chain with proper maintenance will give satisfctory performance. But the maintenance cycle will be what you describe, in my experience.
At this point, check this: On the centerstand, in neutral, press up on the bottom row of the chain to remove ALL slack. Hold this, and at 3:00 oclock on the rear sprocket, grab a pin between thumb and forefinger and pull. If you can see daylight, everything is shot. Time for new (again).
If its not shot, at the rate you are going it soon will be. My suggestion would be to buy new sprockets and give an ORing chain a whirl. It will change your life. IMO
PS: You are lubing the inside of the chain too, not just the outside?